<div class="xblock xblock-public_view xblock-public_view-vertical" data-block-type="vertical" data-runtime-version="1" data-usage-id="block-v1:OCW+6.042J+2T2019+type@vertical+block@0171d64586024509934ef14e9f01862a" data-graded="False" data-runtime-class="LmsRuntime" data-course-id="course-v1:OCW+6.042J+2T2019" data-has-score="False" data-init="VerticalStudentView" data-request-token="7ec97d12dbd311efb03c029b57e3cc89">
<h2 class="hd hd-2 unit-title">Introduction</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:OCW+6.042J+2T2019+type@html+block@d424276db71449d1854bd8ee584c2828">
<div class="xblock xblock-public_view xblock-public_view-html xmodule_display xmodule_HtmlBlock" data-block-type="html" data-runtime-version="1" data-usage-id="block-v1:OCW+6.042J+2T2019+type@html+block@d424276db71449d1854bd8ee584c2828" data-graded="False" data-runtime-class="LmsRuntime" data-course-id="course-v1:OCW+6.042J+2T2019" data-has-score="False" data-init="XBlockToXModuleShim" data-request-token="7ec97d12dbd311efb03c029b57e3cc89">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "HTMLModule"}
</script>
<p>Read <a href="/assets/courseware/v1/3ec8c6b845c29790a13acb31407059da/asset-v1:OCW+6.042J+2T2019+type@asset+block/MIT6_042JS15_Session5.pdf" target="[object Object]">Chapter 3.6 (PDF)</a> of <em>Mathematics for Computer Science</em> for 1.5 Quantifiers & Predicate Logic.</p>
<p>View the <a href="/assets/courseware/v1/9faed471877e2f00828e9c6f6fe94e00/asset-v1:OCW+6.042J+2T2019+type@asset+block/MIT6_042JS15_cp5.pdf" target="[object Object]">Section 1.5 In-Class Questions (PDF)</a></p>
</div>
</div>
</div>
</div>
<div class="xblock xblock-public_view xblock-public_view-vertical" data-block-type="vertical" data-runtime-version="1" data-usage-id="block-v1:OCW+6.042J+2T2019+type@vertical+block@a5e16820e8864b61af587ed848f0617c" data-graded="False" data-runtime-class="LmsRuntime" data-course-id="course-v1:OCW+6.042J+2T2019" data-has-score="False" data-init="VerticalStudentView" data-request-token="7ec97d12dbd311efb03c029b57e3cc89">
<h2 class="hd hd-2 unit-title">Lecture Video | Predicate Logic I</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:OCW+6.042J+2T2019+type@video+block@444efd328bbd4f21ba0851a236438d8f">
<div class="xblock xblock-public_view xblock-public_view-video xmodule_display xmodule_VideoBlock" data-block-type="video" data-runtime-version="1" data-usage-id="block-v1:OCW+6.042J+2T2019+type@video+block@444efd328bbd4f21ba0851a236438d8f" data-graded="False" data-runtime-class="LmsRuntime" data-course-id="course-v1:OCW+6.042J+2T2019" data-has-score="False" data-init="XBlockToXModuleShim" data-request-token="7ec97d12dbd311efb03c029b57e3cc89">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Video"}
</script>
<h3 class="hd hd-2">Predicate Logic I</h3>
<div
id="video_444efd328bbd4f21ba0851a236438d8f"
class="video closed"
data-metadata='{"autoAdvance": false, "transcriptLanguages": {"en": "English"}, "savedVideoPosition": 0.0, "recordedYoutubeIsAvailable": true, "speed": null, "transcriptTranslationUrl": "/courses/course-v1:OCW+6.042J+2T2019/xblock/block-v1:OCW+6.042J+2T2019+type@video+block@444efd328bbd4f21ba0851a236438d8f/handler/transcript/translation/__lang__", "start": 0.0, "showCaptions": "true", "ytTestTimeout": 1500, "saveStateEnabled": false, "transcriptLanguage": "en", "ytApiUrl": "https://www.youtube.com/iframe_api", "generalSpeed": 1.0, "transcriptAvailableTranslationsUrl": "/courses/course-v1:OCW+6.042J+2T2019/xblock/block-v1:OCW+6.042J+2T2019+type@video+block@444efd328bbd4f21ba0851a236438d8f/handler/transcript/available_translations", "completionPercentage": 0.95, "end": 0.0, "lmsRootURL": "https://openlearninglibrary.mit.edu", "sources": ["https://ia800207.us.archive.org/32/items/MIT6.042JS15/MIT6_042JS15_predicatelogic1_ipod.mp4"], "ytMetadataEndpoint": "", "prioritizeHls": false, "autohideHtml5": false, "autoplay": false, "poster": null, "publishCompletionUrl": "/courses/course-v1:OCW+6.042J+2T2019/xblock/block-v1:OCW+6.042J+2T2019+type@video+block@444efd328bbd4f21ba0851a236438d8f/handler/publish_completion", "saveStateUrl": "/courses/course-v1:OCW+6.042J+2T2019/xblock/block-v1:OCW+6.042J+2T2019+type@video+block@444efd328bbd4f21ba0851a236438d8f/handler/xmodule_handler/save_user_state", "duration": 0.0, "captionDataDir": null, "completionEnabled": false, "streams": "1.00:UroprmQHTLc"}'
data-bumper-metadata='null'
data-autoadvance-enabled="False"
data-poster='null'
tabindex="-1"
>
<div class="focus_grabber first"></div>
<div class="tc-wrapper">
<div class="video-wrapper">
<span tabindex="0" class="spinner" aria-hidden="false" aria-label="Loading video player"></span>
<span tabindex="-1" class="btn-play fa fa-youtube-play fa-2x is-hidden" aria-hidden="true" aria-label="Play video"></span>
<div class="video-player-pre"></div>
<div class="video-player">
<div id="444efd328bbd4f21ba0851a236438d8f"></div>
<h4 class="hd hd-4 video-error is-hidden">No playable video sources found.</h4>
<h4 class="hd hd-4 video-hls-error is-hidden">
Your browser does not support this video format. Try using a different browser.
</h4>
</div>
<div class="video-player-post"></div>
<div class="closed-captions"></div>
<div class="video-controls is-hidden">
<div>
<div class="vcr"><div class="vidtime">0:00 / 0:00</div></div>
<div class="secondary-controls"></div>
</div>
</div>
</div>
</div>
<div class="focus_grabber last"></div>
<h3 class="hd hd-4 downloads-heading sr" id="video-download-transcripts_444efd328bbd4f21ba0851a236438d8f">Downloads and transcripts</h3>
<div class="wrapper-downloads" role="region" aria-labelledby="video-download-transcripts_444efd328bbd4f21ba0851a236438d8f">
<div class="wrapper-download-video">
<h4 class="hd hd-5">Video</h4>
<a class="btn-link video-sources video-download-button" href="https://ia800207.us.archive.org/32/items/MIT6.042JS15/MIT6_042JS15_predicatelogic1_ipod.mp4">
Download video file
</a>
</div>
<div class="wrapper-download-transcripts">
<h4 class="hd hd-5">Transcripts</h4>
<ul class="list-download-transcripts">
<li class="transcript-option">
<a class="btn btn-link" href="/courses/course-v1:OCW+6.042J+2T2019/xblock/block-v1:OCW+6.042J+2T2019+type@video+block@444efd328bbd4f21ba0851a236438d8f/handler/transcript/download" data-value="srt">Download SubRip (.srt) file</a>
</li>
<li class="transcript-option">
<a class="btn btn-link" href="/courses/course-v1:OCW+6.042J+2T2019/xblock/block-v1:OCW+6.042J+2T2019+type@video+block@444efd328bbd4f21ba0851a236438d8f/handler/transcript/download" data-value="txt">Download Text (.txt) file</a>
</li>
</ul>
</div>
</div>
</div>
</div>
</div>
<div class="vert vert-1" data-id="block-v1:OCW+6.042J+2T2019+type@html+block@e8e3768008f0432b921ba512e06ff10b">
<div class="xblock xblock-public_view xblock-public_view-html xmodule_display xmodule_HtmlBlock" data-block-type="html" data-runtime-version="1" data-usage-id="block-v1:OCW+6.042J+2T2019+type@html+block@e8e3768008f0432b921ba512e06ff10b" data-graded="False" data-runtime-class="LmsRuntime" data-course-id="course-v1:OCW+6.042J+2T2019" data-has-score="False" data-init="XBlockToXModuleShim" data-request-token="7ec97d12dbd311efb03c029b57e3cc89">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "HTMLModule"}
</script>
<p>Download a copy of the slides for <a href="/assets/courseware/v1/dd3f5d64bd71d66720d23a13e3f2b105/asset-v1:OCW+6.042J+2T2019+type@asset+block/MIT6_042JS16_Predicate_Logic_1.pdf" target="[object Object]">Predicate Logic 1 (PDF)</a></p>
<p><a href="/assets/courseware/v1/acb35aacc8c8710afba98fe0b2e1d18f/asset-v1:OCW+6.042J+2T2019+type@asset+block/Predicate_LogicI_1.5_Lectrans.pdf" target="[object Object]">Lecture video transcript (PDF)</a></p>
</div>
</div>
</div>
</div>
<div class="xblock xblock-public_view xblock-public_view-vertical" data-block-type="vertical" data-runtime-version="1" data-usage-id="block-v1:OCW+6.042J+2T2019+type@vertical+block@c38f125ab3a74f9383e0b4cbaec95128" data-graded="False" data-runtime-class="LmsRuntime" data-course-id="course-v1:OCW+6.042J+2T2019" data-has-score="False" data-init="VerticalStudentView" data-request-token="7ec97d12dbd311efb03c029b57e3cc89">
<h2 class="hd hd-2 unit-title">Lecture Video | Predicate Logic II</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:OCW+6.042J+2T2019+type@video+block@63e72ff742aa42128319d0154a458432">
<div class="xblock xblock-public_view xblock-public_view-video xmodule_display xmodule_VideoBlock" data-block-type="video" data-runtime-version="1" data-usage-id="block-v1:OCW+6.042J+2T2019+type@video+block@63e72ff742aa42128319d0154a458432" data-graded="False" data-runtime-class="LmsRuntime" data-course-id="course-v1:OCW+6.042J+2T2019" data-has-score="False" data-init="XBlockToXModuleShim" data-request-token="7ec97d12dbd311efb03c029b57e3cc89">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Video"}
</script>
<h3 class="hd hd-2">Predicate Logic II</h3>
<div
id="video_63e72ff742aa42128319d0154a458432"
class="video closed"
data-metadata='{"autoAdvance": false, "transcriptLanguages": {"en": "English"}, "savedVideoPosition": 0.0, "recordedYoutubeIsAvailable": true, "speed": null, "transcriptTranslationUrl": "/courses/course-v1:OCW+6.042J+2T2019/xblock/block-v1:OCW+6.042J+2T2019+type@video+block@63e72ff742aa42128319d0154a458432/handler/transcript/translation/__lang__", "start": 0.0, "showCaptions": "true", "ytTestTimeout": 1500, "saveStateEnabled": false, "transcriptLanguage": "en", "ytApiUrl": "https://www.youtube.com/iframe_api", "generalSpeed": 1.0, "transcriptAvailableTranslationsUrl": "/courses/course-v1:OCW+6.042J+2T2019/xblock/block-v1:OCW+6.042J+2T2019+type@video+block@63e72ff742aa42128319d0154a458432/handler/transcript/available_translations", "completionPercentage": 0.95, "end": 0.0, "lmsRootURL": "https://openlearninglibrary.mit.edu", "sources": ["https://ia800207.us.archive.org/32/items/MIT6.042JS15/MIT6_042JS15_predicatelogic2_ipod.mp4"], "ytMetadataEndpoint": "", "prioritizeHls": false, "autohideHtml5": false, "autoplay": false, "poster": null, "publishCompletionUrl": "/courses/course-v1:OCW+6.042J+2T2019/xblock/block-v1:OCW+6.042J+2T2019+type@video+block@63e72ff742aa42128319d0154a458432/handler/publish_completion", "saveStateUrl": "/courses/course-v1:OCW+6.042J+2T2019/xblock/block-v1:OCW+6.042J+2T2019+type@video+block@63e72ff742aa42128319d0154a458432/handler/xmodule_handler/save_user_state", "duration": 0.0, "captionDataDir": null, "completionEnabled": false, "streams": "1.00:T1AtlGrCoU8"}'
data-bumper-metadata='null'
data-autoadvance-enabled="False"
data-poster='null'
tabindex="-1"
>
<div class="focus_grabber first"></div>
<div class="tc-wrapper">
<div class="video-wrapper">
<span tabindex="0" class="spinner" aria-hidden="false" aria-label="Loading video player"></span>
<span tabindex="-1" class="btn-play fa fa-youtube-play fa-2x is-hidden" aria-hidden="true" aria-label="Play video"></span>
<div class="video-player-pre"></div>
<div class="video-player">
<div id="63e72ff742aa42128319d0154a458432"></div>
<h4 class="hd hd-4 video-error is-hidden">No playable video sources found.</h4>
<h4 class="hd hd-4 video-hls-error is-hidden">
Your browser does not support this video format. Try using a different browser.
</h4>
</div>
<div class="video-player-post"></div>
<div class="closed-captions"></div>
<div class="video-controls is-hidden">
<div>
<div class="vcr"><div class="vidtime">0:00 / 0:00</div></div>
<div class="secondary-controls"></div>
</div>
</div>
</div>
</div>
<div class="focus_grabber last"></div>
<h3 class="hd hd-4 downloads-heading sr" id="video-download-transcripts_63e72ff742aa42128319d0154a458432">Downloads and transcripts</h3>
<div class="wrapper-downloads" role="region" aria-labelledby="video-download-transcripts_63e72ff742aa42128319d0154a458432">
<div class="wrapper-download-video">
<h4 class="hd hd-5">Video</h4>
<a class="btn-link video-sources video-download-button" href="https://ia800207.us.archive.org/32/items/MIT6.042JS15/MIT6_042JS15_predicatelogic2_ipod.mp4">
Download video file
</a>
</div>
<div class="wrapper-download-transcripts">
<h4 class="hd hd-5">Transcripts</h4>
<ul class="list-download-transcripts">
<li class="transcript-option">
<a class="btn btn-link" href="/courses/course-v1:OCW+6.042J+2T2019/xblock/block-v1:OCW+6.042J+2T2019+type@video+block@63e72ff742aa42128319d0154a458432/handler/transcript/download" data-value="srt">Download SubRip (.srt) file</a>
</li>
<li class="transcript-option">
<a class="btn btn-link" href="/courses/course-v1:OCW+6.042J+2T2019/xblock/block-v1:OCW+6.042J+2T2019+type@video+block@63e72ff742aa42128319d0154a458432/handler/transcript/download" data-value="txt">Download Text (.txt) file</a>
</li>
</ul>
</div>
</div>
</div>
</div>
</div>
<div class="vert vert-1" data-id="block-v1:OCW+6.042J+2T2019+type@html+block@7227a2e7b8654a62a51f5ddedbf17698">
<div class="xblock xblock-public_view xblock-public_view-html xmodule_display xmodule_HtmlBlock" data-block-type="html" data-runtime-version="1" data-usage-id="block-v1:OCW+6.042J+2T2019+type@html+block@7227a2e7b8654a62a51f5ddedbf17698" data-graded="False" data-runtime-class="LmsRuntime" data-course-id="course-v1:OCW+6.042J+2T2019" data-has-score="False" data-init="XBlockToXModuleShim" data-request-token="7ec97d12dbd311efb03c029b57e3cc89">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "HTMLModule"}
</script>
<p>Download a copy of the slides for <a href="/assets/courseware/v1/44eb7bbabb66be3a1b7c550b2a62d648/asset-v1:OCW+6.042J+2T2019+type@asset+block/MIT6_042JS16_Predicate_Logic_2.pdf" target="[object Object]">Predicate Logic II (PDF)</a></p>
<p><a href="/assets/courseware/v1/4c83771d1ff928a44850488f67abdec3/asset-v1:OCW+6.042J+2T2019+type@asset+block/Predicate_LogicII_Lectrans.pdf" target="[object Object]">Lecture video transcript (PDF)</a></p>
</div>
</div>
</div>
</div>
<div class="xblock xblock-public_view xblock-public_view-vertical" data-block-type="vertical" data-runtime-version="1" data-usage-id="block-v1:OCW+6.042J+2T2019+type@vertical+block@599164aeaa3c49e6b7c67329a66c3a98" data-graded="False" data-runtime-class="LmsRuntime" data-course-id="course-v1:OCW+6.042J+2T2019" data-has-score="False" data-init="VerticalStudentView" data-request-token="7ec97d12dbd311efb03c029b57e3cc89">
<h2 class="hd hd-2 unit-title">Exercise | Satisfiability</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:OCW+6.042J+2T2019+type@problem+block@e9d682fb90cc4aa7b11daa5dbc19ba7a">
<div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-block-type="problem" data-runtime-version="1" data-usage-id="block-v1:OCW+6.042J+2T2019+type@problem+block@e9d682fb90cc4aa7b11daa5dbc19ba7a" data-graded="False" data-runtime-class="LmsRuntime" data-course-id="course-v1:OCW+6.042J+2T2019" data-has-score="True" data-init="XBlockToXModuleShim" data-request-token="7ec97d12dbd311efb03c029b57e3cc89">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Problem"}
</script>
<div id="problem_e9d682fb90cc4aa7b11daa5dbc19ba7a" class="problems-wrapper" role="group"
aria-labelledby="e9d682fb90cc4aa7b11daa5dbc19ba7a-problem-title"
data-problem-id="block-v1:OCW+6.042J+2T2019+type@problem+block@e9d682fb90cc4aa7b11daa5dbc19ba7a" data-url="/courses/course-v1:OCW+6.042J+2T2019/xblock/block-v1:OCW+6.042J+2T2019+type@problem+block@e9d682fb90cc4aa7b11daa5dbc19ba7a/handler/xmodule_handler"
data-problem-score="0"
data-problem-total-possible="1"
data-attempts-used="0"
data-content="
<h3 class="hd hd-3 problem-header" id="e9d682fb90cc4aa7b11daa5dbc19ba7a-problem-title" aria-describedby="block-v1:OCW+6.042J+2T2019+type@problem+block@e9d682fb90cc4aa7b11daa5dbc19ba7a-problem-progress" tabindex="-1">
Satisfiability
</h3>
<div class="problem-progress" id="block-v1:OCW+6.042J+2T2019+type@problem+block@e9d682fb90cc4aa7b11daa5dbc19ba7a-problem-progress"></div>
<div class="problem">
<div>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div class="choicegroup capa_inputtype" id="inputtype_e9d682fb90cc4aa7b11daa5dbc19ba7a_2_1">
<fieldset aria-describedby="status_e9d682fb90cc4aa7b11daa5dbc19ba7a_2_1">
<legend id="e9d682fb90cc4aa7b11daa5dbc19ba7a_2_1-legend" class="response-fieldset-legend field-group-hd">Select all of the options that guarantee that predicate <math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>P</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
</math>is satisfiable:</legend>
<div class="field">
<input type="checkbox" name="input_e9d682fb90cc4aa7b11daa5dbc19ba7a_2_1[]" id="input_e9d682fb90cc4aa7b11daa5dbc19ba7a_2_1_choice_0" class="field-input input-checkbox" value="choice_0"/><label id="e9d682fb90cc4aa7b11daa5dbc19ba7a_2_1-choice_0-label" for="input_e9d682fb90cc4aa7b11daa5dbc19ba7a_2_1_choice_0" class="response-label field-label label-inline" aria-describedby="status_e9d682fb90cc4aa7b11daa5dbc19ba7a_2_1"> <math xmlns="http://www.w3.org/1998/Math/MathML">
<mi mathvariant="normal">&#8704;<!-- &#8704; --></mi>
<mi>x</mi>
<mo>.</mo>
<mi>P</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
</math>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_e9d682fb90cc4aa7b11daa5dbc19ba7a_2_1[]" id="input_e9d682fb90cc4aa7b11daa5dbc19ba7a_2_1_choice_1" class="field-input input-checkbox" value="choice_1"/><label id="e9d682fb90cc4aa7b11daa5dbc19ba7a_2_1-choice_1-label" for="input_e9d682fb90cc4aa7b11daa5dbc19ba7a_2_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_e9d682fb90cc4aa7b11daa5dbc19ba7a_2_1"> <math xmlns="http://www.w3.org/1998/Math/MathML">
<mi mathvariant="normal">&#8707;<!-- &#8707; --></mi>
<mi>x</mi>
<mo>.</mo>
<mi>P</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
</math>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_e9d682fb90cc4aa7b11daa5dbc19ba7a_2_1[]" id="input_e9d682fb90cc4aa7b11daa5dbc19ba7a_2_1_choice_2" class="field-input input-checkbox" value="choice_2"/><label id="e9d682fb90cc4aa7b11daa5dbc19ba7a_2_1-choice_2-label" for="input_e9d682fb90cc4aa7b11daa5dbc19ba7a_2_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_e9d682fb90cc4aa7b11daa5dbc19ba7a_2_1"> <math xmlns="http://www.w3.org/1998/Math/MathML">
<mi mathvariant="normal">&#8704;<!-- &#8704; --></mi>
<mi>x</mi>
<mo>.</mo>
<mtext>NOT</mtext>
<mo stretchy="false">(</mo>
<mi>P</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo stretchy="false">)</mo>
</math>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_e9d682fb90cc4aa7b11daa5dbc19ba7a_2_1[]" id="input_e9d682fb90cc4aa7b11daa5dbc19ba7a_2_1_choice_3" class="field-input input-checkbox" value="choice_3"/><label id="e9d682fb90cc4aa7b11daa5dbc19ba7a_2_1-choice_3-label" for="input_e9d682fb90cc4aa7b11daa5dbc19ba7a_2_1_choice_3" class="response-label field-label label-inline" aria-describedby="status_e9d682fb90cc4aa7b11daa5dbc19ba7a_2_1"> <math xmlns="http://www.w3.org/1998/Math/MathML">
<mtext>NOT</mtext>
<mo stretchy="false">(</mo>
<mi mathvariant="normal">&#8704;<!-- &#8704; --></mi>
<mi>x</mi>
<mo>.</mo>
<mtext>NOT</mtext>
<mo stretchy="false">(</mo>
<mi>P</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo stretchy="false">)</mo>
<mo stretchy="false">)</mo>
</math>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_e9d682fb90cc4aa7b11daa5dbc19ba7a_2_1[]" id="input_e9d682fb90cc4aa7b11daa5dbc19ba7a_2_1_choice_4" class="field-input input-checkbox" value="choice_4"/><label id="e9d682fb90cc4aa7b11daa5dbc19ba7a_2_1-choice_4-label" for="input_e9d682fb90cc4aa7b11daa5dbc19ba7a_2_1_choice_4" class="response-label field-label label-inline" aria-describedby="status_e9d682fb90cc4aa7b11daa5dbc19ba7a_2_1"> <math xmlns="http://www.w3.org/1998/Math/MathML">
<mi mathvariant="normal">&#8707;<!-- &#8707; --></mi>
<mi>x</mi>
<mo>.</mo>
<mtext>NOT</mtext>
<mo stretchy="false">(</mo>
<mi>P</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo stretchy="false">)</mo>
</math>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_e9d682fb90cc4aa7b11daa5dbc19ba7a_2_1[]" id="input_e9d682fb90cc4aa7b11daa5dbc19ba7a_2_1_choice_5" class="field-input input-checkbox" value="choice_5"/><label id="e9d682fb90cc4aa7b11daa5dbc19ba7a_2_1-choice_5-label" for="input_e9d682fb90cc4aa7b11daa5dbc19ba7a_2_1_choice_5" class="response-label field-label label-inline" aria-describedby="status_e9d682fb90cc4aa7b11daa5dbc19ba7a_2_1"> <math xmlns="http://www.w3.org/1998/Math/MathML">
<mtext>NOT</mtext>
<mo stretchy="false">(</mo>
<mi mathvariant="normal">&#8707;<!-- &#8707; --></mi>
<mi>x</mi>
<mo>.</mo>
<mtext>NOT</mtext>
<mo stretchy="false">(</mo>
<mi>P</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo stretchy="false">)</mo>
</math>
</label>
</div>
<span id="answer_e9d682fb90cc4aa7b11daa5dbc19ba7a_2_1"/>
</fieldset>
<div class="indicator-container">
<span class="status unanswered" id="status_e9d682fb90cc4aa7b11daa5dbc19ba7a_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
</div>
</div></div>
</div>
<div class="action">
<input type="hidden" name="problem_id" value="Satisfiability" />
<div class="submit-attempt-container">
<button type="button" class="submit btn-brand" data-submitting="Submitting" data-value="Submit" data-should-enable-submit-button="True" aria-describedby="submission_feedback_e9d682fb90cc4aa7b11daa5dbc19ba7a" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_e9d682fb90cc4aa7b11daa5dbc19ba7a">
<span class="sr">Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.</span>
</div>
</div>
<div class="problem-action-buttons-wrapper">
<span class="problem-action-button-wrapper">
<button type="button" class="reset problem-action-btn btn-default btn-small" data-value="Reset"><span class="icon fa fa-refresh" aria-hidden="true"></span><span aria-hidden="true">Reset</span><span class="sr">Reset your answer</span></button>
</span>
<span class="problem-action-button-wrapper">
<button type="button" class="show problem-action-btn btn-default btn-small" aria-describedby="e9d682fb90cc4aa7b11daa5dbc19ba7a-problem-title"><span class="icon fa fa-info-circle" aria-hidden="true"></span><span class="show-label">Show Answer</span></button>
</span>
</div>
</div>
<div class="notification warning notification-gentle-alert
is-hidden"
tabindex="-1">
<span class="icon fa fa-exclamation-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="e9d682fb90cc4aa7b11daa5dbc19ba7a-problem-title">
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification warning notification-save
is-hidden"
tabindex="-1">
<span class="icon fa fa-save" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="e9d682fb90cc4aa7b11daa5dbc19ba7a-problem-title">None
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification general notification-show-answer
is-hidden"
tabindex="-1">
<span class="icon fa fa-info-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="e9d682fb90cc4aa7b11daa5dbc19ba7a-problem-title">Answers are displayed within the problem
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
</div>
"
data-graded="False">
<p class="loading-spinner">
<i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i>
<span class="sr">Loading…</span>
</p>
</div>
</div>
</div>
</div>
</div>
<div class="xblock xblock-public_view xblock-public_view-vertical" data-block-type="vertical" data-runtime-version="1" data-usage-id="block-v1:OCW+6.042J+2T2019+type@vertical+block@eabd27ab67284d18bc7e923c8fb00d57" data-graded="False" data-runtime-class="LmsRuntime" data-course-id="course-v1:OCW+6.042J+2T2019" data-has-score="False" data-init="VerticalStudentView" data-request-token="7ec97d12dbd311efb03c029b57e3cc89">
<h2 class="hd hd-2 unit-title">Lecture Video | Predicate Logic III</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:OCW+6.042J+2T2019+type@video+block@07a6b48fec8e4e2da1abb54c65c09faa">
<div class="xblock xblock-public_view xblock-public_view-video xmodule_display xmodule_VideoBlock" data-block-type="video" data-runtime-version="1" data-usage-id="block-v1:OCW+6.042J+2T2019+type@video+block@07a6b48fec8e4e2da1abb54c65c09faa" data-graded="False" data-runtime-class="LmsRuntime" data-course-id="course-v1:OCW+6.042J+2T2019" data-has-score="False" data-init="XBlockToXModuleShim" data-request-token="7ec97d12dbd311efb03c029b57e3cc89">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Video"}
</script>
<h3 class="hd hd-2">Predicate Logic III</h3>
<div
id="video_07a6b48fec8e4e2da1abb54c65c09faa"
class="video closed"
data-metadata='{"autoAdvance": false, "transcriptLanguages": {"en": "English"}, "savedVideoPosition": 0.0, "recordedYoutubeIsAvailable": true, "speed": null, "transcriptTranslationUrl": "/courses/course-v1:OCW+6.042J+2T2019/xblock/block-v1:OCW+6.042J+2T2019+type@video+block@07a6b48fec8e4e2da1abb54c65c09faa/handler/transcript/translation/__lang__", "start": 0.0, "showCaptions": "true", "ytTestTimeout": 1500, "saveStateEnabled": false, "transcriptLanguage": "en", "ytApiUrl": "https://www.youtube.com/iframe_api", "generalSpeed": 1.0, "transcriptAvailableTranslationsUrl": "/courses/course-v1:OCW+6.042J+2T2019/xblock/block-v1:OCW+6.042J+2T2019+type@video+block@07a6b48fec8e4e2da1abb54c65c09faa/handler/transcript/available_translations", "completionPercentage": 0.95, "end": 0.0, "lmsRootURL": "https://openlearninglibrary.mit.edu", "sources": ["https://ia800207.us.archive.org/32/items/MIT6.042JS15/MIT6_042JS15_predicatelogic3_ipod.mp4"], "ytMetadataEndpoint": "", "prioritizeHls": false, "autohideHtml5": false, "autoplay": false, "poster": null, "publishCompletionUrl": "/courses/course-v1:OCW+6.042J+2T2019/xblock/block-v1:OCW+6.042J+2T2019+type@video+block@07a6b48fec8e4e2da1abb54c65c09faa/handler/publish_completion", "saveStateUrl": "/courses/course-v1:OCW+6.042J+2T2019/xblock/block-v1:OCW+6.042J+2T2019+type@video+block@07a6b48fec8e4e2da1abb54c65c09faa/handler/xmodule_handler/save_user_state", "duration": 0.0, "captionDataDir": null, "completionEnabled": false, "streams": "1.00:L5uBeAGJV1k"}'
data-bumper-metadata='null'
data-autoadvance-enabled="False"
data-poster='null'
tabindex="-1"
>
<div class="focus_grabber first"></div>
<div class="tc-wrapper">
<div class="video-wrapper">
<span tabindex="0" class="spinner" aria-hidden="false" aria-label="Loading video player"></span>
<span tabindex="-1" class="btn-play fa fa-youtube-play fa-2x is-hidden" aria-hidden="true" aria-label="Play video"></span>
<div class="video-player-pre"></div>
<div class="video-player">
<div id="07a6b48fec8e4e2da1abb54c65c09faa"></div>
<h4 class="hd hd-4 video-error is-hidden">No playable video sources found.</h4>
<h4 class="hd hd-4 video-hls-error is-hidden">
Your browser does not support this video format. Try using a different browser.
</h4>
</div>
<div class="video-player-post"></div>
<div class="closed-captions"></div>
<div class="video-controls is-hidden">
<div>
<div class="vcr"><div class="vidtime">0:00 / 0:00</div></div>
<div class="secondary-controls"></div>
</div>
</div>
</div>
</div>
<div class="focus_grabber last"></div>
<h3 class="hd hd-4 downloads-heading sr" id="video-download-transcripts_07a6b48fec8e4e2da1abb54c65c09faa">Downloads and transcripts</h3>
<div class="wrapper-downloads" role="region" aria-labelledby="video-download-transcripts_07a6b48fec8e4e2da1abb54c65c09faa">
<div class="wrapper-download-video">
<h4 class="hd hd-5">Video</h4>
<a class="btn-link video-sources video-download-button" href="https://ia800207.us.archive.org/32/items/MIT6.042JS15/MIT6_042JS15_predicatelogic3_ipod.mp4">
Download video file
</a>
</div>
<div class="wrapper-download-transcripts">
<h4 class="hd hd-5">Transcripts</h4>
<ul class="list-download-transcripts">
<li class="transcript-option">
<a class="btn btn-link" href="/courses/course-v1:OCW+6.042J+2T2019/xblock/block-v1:OCW+6.042J+2T2019+type@video+block@07a6b48fec8e4e2da1abb54c65c09faa/handler/transcript/download" data-value="srt">Download SubRip (.srt) file</a>
</li>
<li class="transcript-option">
<a class="btn btn-link" href="/courses/course-v1:OCW+6.042J+2T2019/xblock/block-v1:OCW+6.042J+2T2019+type@video+block@07a6b48fec8e4e2da1abb54c65c09faa/handler/transcript/download" data-value="txt">Download Text (.txt) file</a>
</li>
</ul>
</div>
</div>
</div>
</div>
</div>
<div class="vert vert-1" data-id="block-v1:OCW+6.042J+2T2019+type@html+block@9bad677e9f2645038f9f32660936bc71">
<div class="xblock xblock-public_view xblock-public_view-html xmodule_display xmodule_HtmlBlock" data-block-type="html" data-runtime-version="1" data-usage-id="block-v1:OCW+6.042J+2T2019+type@html+block@9bad677e9f2645038f9f32660936bc71" data-graded="False" data-runtime-class="LmsRuntime" data-course-id="course-v1:OCW+6.042J+2T2019" data-has-score="False" data-init="XBlockToXModuleShim" data-request-token="7ec97d12dbd311efb03c029b57e3cc89">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "HTMLModule"}
</script>
<p>Download a copy of the slides for <a href="/assets/courseware/v1/1ef977ce96deb971dacf8bf4464f538f/asset-v1:OCW+6.042J+2T2019+type@asset+block/MIT6_042JS16_Predicate_Logic_3.pdf" target="[object Object]">Predicate Logic III (PDF)</a></p>
<p><a href="/assets/courseware/v1/ae6c36377180d73da67e6fe3a9d3ffad/asset-v1:OCW+6.042J+2T2019+type@asset+block/Predicate_Logic_III_Lectrans.pdf" target="[object Object]">Lecture video transcript (PDF)</a></p>
</div>
</div>
</div>
</div>
<div class="xblock xblock-public_view xblock-public_view-vertical" data-block-type="vertical" data-runtime-version="1" data-usage-id="block-v1:OCW+6.042J+2T2019+type@vertical+block@039d07d9d8a346c799f7361ef66f979f" data-graded="False" data-runtime-class="LmsRuntime" data-course-id="course-v1:OCW+6.042J+2T2019" data-has-score="False" data-init="VerticalStudentView" data-request-token="7ec97d12dbd311efb03c029b57e3cc89">
<h2 class="hd hd-2 unit-title">Exercise | Name That Predicate!</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:OCW+6.042J+2T2019+type@problem+block@1db820e976dc48699b922a236b790e4d">
<div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-block-type="problem" data-runtime-version="1" data-usage-id="block-v1:OCW+6.042J+2T2019+type@problem+block@1db820e976dc48699b922a236b790e4d" data-graded="False" data-runtime-class="LmsRuntime" data-course-id="course-v1:OCW+6.042J+2T2019" data-has-score="True" data-init="XBlockToXModuleShim" data-request-token="7ec97d12dbd311efb03c029b57e3cc89">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Problem"}
</script>
<div id="problem_1db820e976dc48699b922a236b790e4d" class="problems-wrapper" role="group"
aria-labelledby="1db820e976dc48699b922a236b790e4d-problem-title"
data-problem-id="block-v1:OCW+6.042J+2T2019+type@problem+block@1db820e976dc48699b922a236b790e4d" data-url="/courses/course-v1:OCW+6.042J+2T2019/xblock/block-v1:OCW+6.042J+2T2019+type@problem+block@1db820e976dc48699b922a236b790e4d/handler/xmodule_handler"
data-problem-score="0"
data-problem-total-possible="1"
data-attempts-used="0"
data-content="
<h3 class="hd hd-3 problem-header" id="1db820e976dc48699b922a236b790e4d-problem-title" aria-describedby="block-v1:OCW+6.042J+2T2019+type@problem+block@1db820e976dc48699b922a236b790e4d-problem-progress" tabindex="-1">
Name That Predicate!
</h3>
<div class="problem-progress" id="block-v1:OCW+6.042J+2T2019+type@problem+block@1db820e976dc48699b922a236b790e4d-problem-progress"></div>
<div class="problem">
<div>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div class="choicegroup capa_inputtype" id="inputtype_1db820e976dc48699b922a236b790e4d_2_1">
<fieldset aria-describedby="status_1db820e976dc48699b922a236b790e4d_2_1">
<legend id="1db820e976dc48699b922a236b790e4d_2_1-legend" class="response-fieldset-legend field-group-hd">We have a procedure to fix any problem.
If the range of <math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>p</mi>
</math> is the set of procedures and <math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>i</mi>
</math> is in the set of issues, pick the quantifiers that complete the statement.
_____.<math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>p</mi>
</math> fixes <math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>i</mi>
</math></legend>
<div class="field">
<input type="radio" name="input_1db820e976dc48699b922a236b790e4d_2_1" id="input_1db820e976dc48699b922a236b790e4d_2_1_choice_0" class="field-input input-radio" value="choice_0"/><label id="1db820e976dc48699b922a236b790e4d_2_1-choice_0-label" for="input_1db820e976dc48699b922a236b790e4d_2_1_choice_0" class="response-label field-label label-inline" aria-describedby="status_1db820e976dc48699b922a236b790e4d_2_1"> <math xmlns="http://www.w3.org/1998/Math/MathML">
<mi mathvariant="normal">&#8704;<!-- &#8704; --></mi>
<mi>p</mi>
<mi mathvariant="normal">&#8707;<!-- &#8707; --></mi>
<mi>i</mi>
</math>
</label>
</div>
<div class="field">
<input type="radio" name="input_1db820e976dc48699b922a236b790e4d_2_1" id="input_1db820e976dc48699b922a236b790e4d_2_1_choice_1" class="field-input input-radio" value="choice_1"/><label id="1db820e976dc48699b922a236b790e4d_2_1-choice_1-label" for="input_1db820e976dc48699b922a236b790e4d_2_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_1db820e976dc48699b922a236b790e4d_2_1"> <math xmlns="http://www.w3.org/1998/Math/MathML">
<mi mathvariant="normal">&#8707;<!-- &#8707; --></mi>
<mi>p</mi>
<mi mathvariant="normal">&#8704;<!-- &#8704; --></mi>
<mi>i</mi>
</math>
</label>
</div>
<div class="field">
<input type="radio" name="input_1db820e976dc48699b922a236b790e4d_2_1" id="input_1db820e976dc48699b922a236b790e4d_2_1_choice_2" class="field-input input-radio" value="choice_2"/><label id="1db820e976dc48699b922a236b790e4d_2_1-choice_2-label" for="input_1db820e976dc48699b922a236b790e4d_2_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_1db820e976dc48699b922a236b790e4d_2_1"> <math xmlns="http://www.w3.org/1998/Math/MathML">
<mi mathvariant="normal">&#8704;<!-- &#8704; --></mi>
<mi>p</mi>
<mi mathvariant="normal">&#8704;<!-- &#8704; --></mi>
<mi>i</mi>
</math>
</label>
</div>
<div class="field">
<input type="radio" name="input_1db820e976dc48699b922a236b790e4d_2_1" id="input_1db820e976dc48699b922a236b790e4d_2_1_choice_3" class="field-input input-radio" value="choice_3"/><label id="1db820e976dc48699b922a236b790e4d_2_1-choice_3-label" for="input_1db820e976dc48699b922a236b790e4d_2_1_choice_3" class="response-label field-label label-inline" aria-describedby="status_1db820e976dc48699b922a236b790e4d_2_1"> <math xmlns="http://www.w3.org/1998/Math/MathML">
<mi mathvariant="normal">&#8704;<!-- &#8704; --></mi>
<mi>i</mi>
<mi mathvariant="normal">&#8707;<!-- &#8707; --></mi>
<mi>p</mi>
</math>
</label>
</div>
<div class="field">
<input type="radio" name="input_1db820e976dc48699b922a236b790e4d_2_1" id="input_1db820e976dc48699b922a236b790e4d_2_1_choice_4" class="field-input input-radio" value="choice_4"/><label id="1db820e976dc48699b922a236b790e4d_2_1-choice_4-label" for="input_1db820e976dc48699b922a236b790e4d_2_1_choice_4" class="response-label field-label label-inline" aria-describedby="status_1db820e976dc48699b922a236b790e4d_2_1"> <math xmlns="http://www.w3.org/1998/Math/MathML">
<mi mathvariant="normal">&#8707;<!-- &#8707; --></mi>
<mi>i</mi>
<mi mathvariant="normal">&#8704;<!-- &#8704; --></mi>
<mi>p</mi>
</math>
</label>
</div>
<div class="field">
<input type="radio" name="input_1db820e976dc48699b922a236b790e4d_2_1" id="input_1db820e976dc48699b922a236b790e4d_2_1_choice_5" class="field-input input-radio" value="choice_5"/><label id="1db820e976dc48699b922a236b790e4d_2_1-choice_5-label" for="input_1db820e976dc48699b922a236b790e4d_2_1_choice_5" class="response-label field-label label-inline" aria-describedby="status_1db820e976dc48699b922a236b790e4d_2_1"> <math xmlns="http://www.w3.org/1998/Math/MathML">
<mi mathvariant="normal">&#8704;<!-- &#8704; --></mi>
<mi>i</mi>
<mi mathvariant="normal">&#8704;<!-- &#8704; --></mi>
<mi>p</mi>
</math>
</label>
</div>
<span id="answer_1db820e976dc48699b922a236b790e4d_2_1"/>
</fieldset>
<div class="indicator-container">
<span class="status unanswered" id="status_1db820e976dc48699b922a236b790e4d_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
</div>
</div></div>
</div>
<div class="action">
<input type="hidden" name="problem_id" value="Name That Predicate!" />
<div class="submit-attempt-container">
<button type="button" class="submit btn-brand" data-submitting="Submitting" data-value="Submit" data-should-enable-submit-button="True" aria-describedby="submission_feedback_1db820e976dc48699b922a236b790e4d" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_1db820e976dc48699b922a236b790e4d">
<span class="sr">Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.</span>
</div>
</div>
<div class="problem-action-buttons-wrapper">
<span class="problem-action-button-wrapper">
<button type="button" class="reset problem-action-btn btn-default btn-small" data-value="Reset"><span class="icon fa fa-refresh" aria-hidden="true"></span><span aria-hidden="true">Reset</span><span class="sr">Reset your answer</span></button>
</span>
<span class="problem-action-button-wrapper">
<button type="button" class="show problem-action-btn btn-default btn-small" aria-describedby="1db820e976dc48699b922a236b790e4d-problem-title"><span class="icon fa fa-info-circle" aria-hidden="true"></span><span class="show-label">Show Answer</span></button>
</span>
</div>
</div>
<div class="notification warning notification-gentle-alert
is-hidden"
tabindex="-1">
<span class="icon fa fa-exclamation-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="1db820e976dc48699b922a236b790e4d-problem-title">
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification warning notification-save
is-hidden"
tabindex="-1">
<span class="icon fa fa-save" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="1db820e976dc48699b922a236b790e4d-problem-title">None
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification general notification-show-answer
is-hidden"
tabindex="-1">
<span class="icon fa fa-info-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="1db820e976dc48699b922a236b790e4d-problem-title">Answers are displayed within the problem
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
</div>
"
data-graded="False">
<p class="loading-spinner">
<i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i>
<span class="sr">Loading…</span>
</p>
</div>
</div>
</div>
</div>
</div>
<div class="xblock xblock-public_view xblock-public_view-vertical" data-block-type="vertical" data-runtime-version="1" data-usage-id="block-v1:OCW+6.042J+2T2019+type@vertical+block@055feeae90e3497b86dd8986812b2623" data-graded="False" data-runtime-class="LmsRuntime" data-course-id="course-v1:OCW+6.042J+2T2019" data-has-score="False" data-init="VerticalStudentView" data-request-token="7ec97d12dbd311efb03c029b57e3cc89">
<h2 class="hd hd-2 unit-title">Exercise | Quantifiers</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:OCW+6.042J+2T2019+type@problem+block@8f340c4a5ccc4867b78e3be6c79a3966">
<div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-block-type="problem" data-runtime-version="1" data-usage-id="block-v1:OCW+6.042J+2T2019+type@problem+block@8f340c4a5ccc4867b78e3be6c79a3966" data-graded="False" data-runtime-class="LmsRuntime" data-course-id="course-v1:OCW+6.042J+2T2019" data-has-score="True" data-init="XBlockToXModuleShim" data-request-token="7ec97d12dbd311efb03c029b57e3cc89">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Problem"}
</script>
<div id="problem_8f340c4a5ccc4867b78e3be6c79a3966" class="problems-wrapper" role="group"
aria-labelledby="8f340c4a5ccc4867b78e3be6c79a3966-problem-title"
data-problem-id="block-v1:OCW+6.042J+2T2019+type@problem+block@8f340c4a5ccc4867b78e3be6c79a3966" data-url="/courses/course-v1:OCW+6.042J+2T2019/xblock/block-v1:OCW+6.042J+2T2019+type@problem+block@8f340c4a5ccc4867b78e3be6c79a3966/handler/xmodule_handler"
data-problem-score="0"
data-problem-total-possible="1"
data-attempts-used="0"
data-content="
<h3 class="hd hd-3 problem-header" id="8f340c4a5ccc4867b78e3be6c79a3966-problem-title" aria-describedby="block-v1:OCW+6.042J+2T2019+type@problem+block@8f340c4a5ccc4867b78e3be6c79a3966-problem-progress" tabindex="-1">
Quantifiers
</h3>
<div class="problem-progress" id="block-v1:OCW+6.042J+2T2019+type@problem+block@8f340c4a5ccc4867b78e3be6c79a3966-problem-progress"></div>
<div class="problem">
<div>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div class="choicegroup capa_inputtype" id="inputtype_8f340c4a5ccc4867b78e3be6c79a3966_2_1">
<fieldset aria-describedby="status_8f340c4a5ccc4867b78e3be6c79a3966_2_1">
<legend id="8f340c4a5ccc4867b78e3be6c79a3966_2_1-legend" class="response-fieldset-legend field-group-hd">Let <math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>Q</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo>,</mo>
<mi>y</mi>
<mo stretchy="false">)</mo>
</math> be the statement
<br/>
<br/>
"<math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>x</mi>
</math> has been a contestant on television show <math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>y</mi>
</math>."
<br/>
<br/>
The domain of discourse for <math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>x</mi>
</math> is the set of all students at your school and for <math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>y</mi>
</math> is the set of all quiz shows on television.
<br/>
<br/>
Which of the following are logically equivalent to:
<center>"No student at your school has ever been a contestant on a television quiz show."</center></legend>
<div class="field">
<input type="checkbox" name="input_8f340c4a5ccc4867b78e3be6c79a3966_2_1[]" id="input_8f340c4a5ccc4867b78e3be6c79a3966_2_1_choice_0" class="field-input input-checkbox" value="choice_0"/><label id="8f340c4a5ccc4867b78e3be6c79a3966_2_1-choice_0-label" for="input_8f340c4a5ccc4867b78e3be6c79a3966_2_1_choice_0" class="response-label field-label label-inline" aria-describedby="status_8f340c4a5ccc4867b78e3be6c79a3966_2_1"> <math xmlns="http://www.w3.org/1998/Math/MathML">
<mi mathvariant="normal">&#8704;<!-- &#8704; --></mi>
<mi>x</mi>
<mi mathvariant="normal">&#8704;<!-- &#8704; --></mi>
<mi>y</mi>
<mo>.</mo>
<mtext>NOT</mtext>
<mo stretchy="false">(</mo>
<mi>Q</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo>,</mo>
<mi>y</mi>
<mo stretchy="false">)</mo>
<mo stretchy="false">)</mo>
</math>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_8f340c4a5ccc4867b78e3be6c79a3966_2_1[]" id="input_8f340c4a5ccc4867b78e3be6c79a3966_2_1_choice_1" class="field-input input-checkbox" value="choice_1"/><label id="8f340c4a5ccc4867b78e3be6c79a3966_2_1-choice_1-label" for="input_8f340c4a5ccc4867b78e3be6c79a3966_2_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_8f340c4a5ccc4867b78e3be6c79a3966_2_1"> <math xmlns="http://www.w3.org/1998/Math/MathML">
<mi mathvariant="normal">&#8707;<!-- &#8707; --></mi>
<mi>x</mi>
<mi mathvariant="normal">&#8707;<!-- &#8707; --></mi>
<mi>y</mi>
<mo>.</mo>
<mtext>NOT</mtext>
<mo stretchy="false">(</mo>
<mi>Q</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo>,</mo>
<mi>y</mi>
<mo stretchy="false">)</mo>
<mo stretchy="false">)</mo>
</math>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_8f340c4a5ccc4867b78e3be6c79a3966_2_1[]" id="input_8f340c4a5ccc4867b78e3be6c79a3966_2_1_choice_2" class="field-input input-checkbox" value="choice_2"/><label id="8f340c4a5ccc4867b78e3be6c79a3966_2_1-choice_2-label" for="input_8f340c4a5ccc4867b78e3be6c79a3966_2_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_8f340c4a5ccc4867b78e3be6c79a3966_2_1"> <math xmlns="http://www.w3.org/1998/Math/MathML">
<mtext>NOT</mtext>
<mo stretchy="false">(</mo>
<mi mathvariant="normal">&#8704;<!-- &#8704; --></mi>
<mi>x</mi>
<mi mathvariant="normal">&#8704;<!-- &#8704; --></mi>
<mi>y</mi>
<mo>.</mo>
<mi>Q</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo>,</mo>
<mi>y</mi>
<mo stretchy="false">)</mo>
<mo stretchy="false">)</mo>
</math>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_8f340c4a5ccc4867b78e3be6c79a3966_2_1[]" id="input_8f340c4a5ccc4867b78e3be6c79a3966_2_1_choice_3" class="field-input input-checkbox" value="choice_3"/><label id="8f340c4a5ccc4867b78e3be6c79a3966_2_1-choice_3-label" for="input_8f340c4a5ccc4867b78e3be6c79a3966_2_1_choice_3" class="response-label field-label label-inline" aria-describedby="status_8f340c4a5ccc4867b78e3be6c79a3966_2_1"> <math xmlns="http://www.w3.org/1998/Math/MathML">
<mtext>NOT</mtext>
<mo stretchy="false">(</mo>
<mi mathvariant="normal">&#8707;<!-- &#8707; --></mi>
<mi>x</mi>
<mi mathvariant="normal">&#8707;<!-- &#8707; --></mi>
<mi>y</mi>
<mo>.</mo>
<mi>Q</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo>,</mo>
<mi>y</mi>
<mo stretchy="false">)</mo>
<mo stretchy="false">)</mo>
</math>
</label>
</div>
<span id="answer_8f340c4a5ccc4867b78e3be6c79a3966_2_1"/>
</fieldset>
<div class="indicator-container">
<span class="status unanswered" id="status_8f340c4a5ccc4867b78e3be6c79a3966_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
</div>
</div></div>
</div>
<div class="action">
<input type="hidden" name="problem_id" value="Quantifiers" />
<div class="submit-attempt-container">
<button type="button" class="submit btn-brand" data-submitting="Submitting" data-value="Submit" data-should-enable-submit-button="True" aria-describedby="submission_feedback_8f340c4a5ccc4867b78e3be6c79a3966" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_8f340c4a5ccc4867b78e3be6c79a3966">
<span class="sr">Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.</span>
</div>
</div>
<div class="problem-action-buttons-wrapper">
<span class="problem-action-button-wrapper">
<button type="button" class="reset problem-action-btn btn-default btn-small" data-value="Reset"><span class="icon fa fa-refresh" aria-hidden="true"></span><span aria-hidden="true">Reset</span><span class="sr">Reset your answer</span></button>
</span>
<span class="problem-action-button-wrapper">
<button type="button" class="show problem-action-btn btn-default btn-small" aria-describedby="8f340c4a5ccc4867b78e3be6c79a3966-problem-title"><span class="icon fa fa-info-circle" aria-hidden="true"></span><span class="show-label">Show Answer</span></button>
</span>
</div>
</div>
<div class="notification warning notification-gentle-alert
is-hidden"
tabindex="-1">
<span class="icon fa fa-exclamation-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="8f340c4a5ccc4867b78e3be6c79a3966-problem-title">
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification warning notification-save
is-hidden"
tabindex="-1">
<span class="icon fa fa-save" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="8f340c4a5ccc4867b78e3be6c79a3966-problem-title">None
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification general notification-show-answer
is-hidden"
tabindex="-1">
<span class="icon fa fa-info-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="8f340c4a5ccc4867b78e3be6c79a3966-problem-title">Answers are displayed within the problem
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
</div>
"
data-graded="False">
<p class="loading-spinner">
<i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i>
<span class="sr">Loading…</span>
</p>
</div>
</div>
</div>
</div>
</div>
<div class="xblock xblock-public_view xblock-public_view-vertical" data-block-type="vertical" data-runtime-version="1" data-usage-id="block-v1:OCW+6.042J+2T2019+type@vertical+block@3d46eb65a6e24deab32002d1c9ecab4a" data-graded="False" data-runtime-class="LmsRuntime" data-course-id="course-v1:OCW+6.042J+2T2019" data-has-score="False" data-init="VerticalStudentView" data-request-token="7ec97d12dbd311efb03c029b57e3cc89">
<h2 class="hd hd-2 unit-title">Exercise | Propositions with Quantifiers</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:OCW+6.042J+2T2019+type@problem+block@c70ffbdf44f04efdbdf3f5310beec8a3">
<div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-block-type="problem" data-runtime-version="1" data-usage-id="block-v1:OCW+6.042J+2T2019+type@problem+block@c70ffbdf44f04efdbdf3f5310beec8a3" data-graded="False" data-runtime-class="LmsRuntime" data-course-id="course-v1:OCW+6.042J+2T2019" data-has-score="True" data-init="XBlockToXModuleShim" data-request-token="7ec97d12dbd311efb03c029b57e3cc89">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Problem"}
</script>
<div id="problem_c70ffbdf44f04efdbdf3f5310beec8a3" class="problems-wrapper" role="group"
aria-labelledby="c70ffbdf44f04efdbdf3f5310beec8a3-problem-title"
data-problem-id="block-v1:OCW+6.042J+2T2019+type@problem+block@c70ffbdf44f04efdbdf3f5310beec8a3" data-url="/courses/course-v1:OCW+6.042J+2T2019/xblock/block-v1:OCW+6.042J+2T2019+type@problem+block@c70ffbdf44f04efdbdf3f5310beec8a3/handler/xmodule_handler"
data-problem-score="0"
data-problem-total-possible="3"
data-attempts-used="0"
data-content="
<h3 class="hd hd-3 problem-header" id="c70ffbdf44f04efdbdf3f5310beec8a3-problem-title" aria-describedby="block-v1:OCW+6.042J+2T2019+type@problem+block@c70ffbdf44f04efdbdf3f5310beec8a3-problem-progress" tabindex="-1">
Propositions with Quantifiers
</h3>
<div class="problem-progress" id="block-v1:OCW+6.042J+2T2019+type@problem+block@c70ffbdf44f04efdbdf3f5310beec8a3-problem-progress"></div>
<div class="problem">
<div>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><p><b> Determine which propositions are true when the variables range over: </b> </p>
<p> 1. The nonnegative integers </p>
<div class="choicegroup capa_inputtype" id="inputtype_c70ffbdf44f04efdbdf3f5310beec8a3_2_1">
<fieldset aria-describedby="status_c70ffbdf44f04efdbdf3f5310beec8a3_2_1">
<div class="field">
<input type="checkbox" name="input_c70ffbdf44f04efdbdf3f5310beec8a3_2_1[]" id="input_c70ffbdf44f04efdbdf3f5310beec8a3_2_1_choice_0" class="field-input input-checkbox" value="choice_0"/><label id="c70ffbdf44f04efdbdf3f5310beec8a3_2_1-choice_0-label" for="input_c70ffbdf44f04efdbdf3f5310beec8a3_2_1_choice_0" class="response-label field-label label-inline" aria-describedby="status_c70ffbdf44f04efdbdf3f5310beec8a3_2_1"> <math xmlns="http://www.w3.org/1998/Math/MathML">
<mi mathvariant="normal">&#8704;<!-- &#8704; --></mi>
<mi>x</mi>
<mi mathvariant="normal">&#8707;<!-- &#8707; --></mi>
<mi>y</mi>
<mo>.</mo>
<mn>2</mn>
<mi>x</mi>
<mo>&#8722;<!-- &#8722; --></mo>
<mi>y</mi>
<mo>=</mo>
<mn>0</mn>
</math>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_c70ffbdf44f04efdbdf3f5310beec8a3_2_1[]" id="input_c70ffbdf44f04efdbdf3f5310beec8a3_2_1_choice_1" class="field-input input-checkbox" value="choice_1"/><label id="c70ffbdf44f04efdbdf3f5310beec8a3_2_1-choice_1-label" for="input_c70ffbdf44f04efdbdf3f5310beec8a3_2_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_c70ffbdf44f04efdbdf3f5310beec8a3_2_1"> <math xmlns="http://www.w3.org/1998/Math/MathML">
<mi mathvariant="normal">&#8704;<!-- &#8704; --></mi>
<mi>x</mi>
<mi mathvariant="normal">&#8707;<!-- &#8707; --></mi>
<mi>y</mi>
<mo>.</mo>
<mi>x</mi>
<mo>&#8722;<!-- &#8722; --></mo>
<mn>2</mn>
<mi>y</mi>
<mo>=</mo>
<mn>0</mn>
</math>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_c70ffbdf44f04efdbdf3f5310beec8a3_2_1[]" id="input_c70ffbdf44f04efdbdf3f5310beec8a3_2_1_choice_2" class="field-input input-checkbox" value="choice_2"/><label id="c70ffbdf44f04efdbdf3f5310beec8a3_2_1-choice_2-label" for="input_c70ffbdf44f04efdbdf3f5310beec8a3_2_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_c70ffbdf44f04efdbdf3f5310beec8a3_2_1"> <math xmlns="http://www.w3.org/1998/Math/MathML">
<mi mathvariant="normal">&#8704;<!-- &#8704; --></mi>
<mi>x</mi>
<mo>.</mo>
<mi>x</mi>
<mo>&lt;</mo>
<mn>10</mn>
<mtext>&#160;IMPLIES&#160;</mtext>
<mo stretchy="false">[</mo>
<mi mathvariant="normal">&#8704;<!-- &#8704; --></mi>
<mi>y</mi>
<mo>.</mo>
<mi>y</mi>
<mo>&lt;</mo>
<mi>x</mi>
<mtext>&#160;IMPLIES&#160;</mtext>
<mi>y</mi>
<mo>&lt;</mo>
<mn>9</mn>
<mo stretchy="false">]</mo>
</math>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_c70ffbdf44f04efdbdf3f5310beec8a3_2_1[]" id="input_c70ffbdf44f04efdbdf3f5310beec8a3_2_1_choice_3" class="field-input input-checkbox" value="choice_3"/><label id="c70ffbdf44f04efdbdf3f5310beec8a3_2_1-choice_3-label" for="input_c70ffbdf44f04efdbdf3f5310beec8a3_2_1_choice_3" class="response-label field-label label-inline" aria-describedby="status_c70ffbdf44f04efdbdf3f5310beec8a3_2_1"> <math xmlns="http://www.w3.org/1998/Math/MathML">
<mi mathvariant="normal">&#8704;<!-- &#8704; --></mi>
<mi>x</mi>
<mi mathvariant="normal">&#8707;<!-- &#8707; --></mi>
<mi>y</mi>
<mo>.</mo>
<mo stretchy="false">[</mo>
<mi>y</mi>
<mo>&gt;</mo>
<mi>x</mi>
<mtext>&#160;AND&#160;</mtext>
<mi mathvariant="normal">&#8707;<!-- &#8707; --></mi>
<mi>z</mi>
<mo>.</mo>
<mi>y</mi>
<mo>+</mo>
<mi>z</mi>
<mo>=</mo>
<mn>100</mn>
<mo stretchy="false">]</mo>
</math>
</label>
</div>
<span id="answer_c70ffbdf44f04efdbdf3f5310beec8a3_2_1"/>
</fieldset>
<div class="indicator-container">
<span class="status unanswered" id="status_c70ffbdf44f04efdbdf3f5310beec8a3_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
</div>
</div></div>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 2" role="group"><p> 2. The integers </p>
<div class="choicegroup capa_inputtype" id="inputtype_c70ffbdf44f04efdbdf3f5310beec8a3_3_1">
<fieldset aria-describedby="status_c70ffbdf44f04efdbdf3f5310beec8a3_3_1">
<div class="field">
<input type="checkbox" name="input_c70ffbdf44f04efdbdf3f5310beec8a3_3_1[]" id="input_c70ffbdf44f04efdbdf3f5310beec8a3_3_1_choice_0" class="field-input input-checkbox" value="choice_0"/><label id="c70ffbdf44f04efdbdf3f5310beec8a3_3_1-choice_0-label" for="input_c70ffbdf44f04efdbdf3f5310beec8a3_3_1_choice_0" class="response-label field-label label-inline" aria-describedby="status_c70ffbdf44f04efdbdf3f5310beec8a3_3_1"> <math xmlns="http://www.w3.org/1998/Math/MathML">
<mi mathvariant="normal">&#8704;<!-- &#8704; --></mi>
<mi>x</mi>
<mi mathvariant="normal">&#8707;<!-- &#8707; --></mi>
<mi>y</mi>
<mo>.</mo>
<mn>2</mn>
<mi>x</mi>
<mo>&#8722;<!-- &#8722; --></mo>
<mi>y</mi>
<mo>=</mo>
<mn>0</mn>
</math>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_c70ffbdf44f04efdbdf3f5310beec8a3_3_1[]" id="input_c70ffbdf44f04efdbdf3f5310beec8a3_3_1_choice_1" class="field-input input-checkbox" value="choice_1"/><label id="c70ffbdf44f04efdbdf3f5310beec8a3_3_1-choice_1-label" for="input_c70ffbdf44f04efdbdf3f5310beec8a3_3_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_c70ffbdf44f04efdbdf3f5310beec8a3_3_1"> <math xmlns="http://www.w3.org/1998/Math/MathML">
<mi mathvariant="normal">&#8704;<!-- &#8704; --></mi>
<mi>x</mi>
<mi mathvariant="normal">&#8707;<!-- &#8707; --></mi>
<mi>y</mi>
<mo>.</mo>
<mi>x</mi>
<mo>&#8722;<!-- &#8722; --></mo>
<mn>2</mn>
<mi>y</mi>
<mo>=</mo>
<mn>0</mn>
</math>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_c70ffbdf44f04efdbdf3f5310beec8a3_3_1[]" id="input_c70ffbdf44f04efdbdf3f5310beec8a3_3_1_choice_2" class="field-input input-checkbox" value="choice_2"/><label id="c70ffbdf44f04efdbdf3f5310beec8a3_3_1-choice_2-label" for="input_c70ffbdf44f04efdbdf3f5310beec8a3_3_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_c70ffbdf44f04efdbdf3f5310beec8a3_3_1"> <math xmlns="http://www.w3.org/1998/Math/MathML">
<mi mathvariant="normal">&#8704;<!-- &#8704; --></mi>
<mi>x</mi>
<mo>.</mo>
<mi>x</mi>
<mo>&lt;</mo>
<mn>10</mn>
<mtext>&#160;IMPLIES&#160;</mtext>
<mo stretchy="false">[</mo>
<mi mathvariant="normal">&#8704;<!-- &#8704; --></mi>
<mi>y</mi>
<mo>.</mo>
<mi>y</mi>
<mo>&lt;</mo>
<mi>x</mi>
<mtext>&#160;IMPLIES&#160;</mtext>
<mi>y</mi>
<mo>&lt;</mo>
<mn>9</mn>
<mo stretchy="false">]</mo>
</math>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_c70ffbdf44f04efdbdf3f5310beec8a3_3_1[]" id="input_c70ffbdf44f04efdbdf3f5310beec8a3_3_1_choice_3" class="field-input input-checkbox" value="choice_3"/><label id="c70ffbdf44f04efdbdf3f5310beec8a3_3_1-choice_3-label" for="input_c70ffbdf44f04efdbdf3f5310beec8a3_3_1_choice_3" class="response-label field-label label-inline" aria-describedby="status_c70ffbdf44f04efdbdf3f5310beec8a3_3_1"> <math xmlns="http://www.w3.org/1998/Math/MathML">
<mi mathvariant="normal">&#8704;<!-- &#8704; --></mi>
<mi>x</mi>
<mi mathvariant="normal">&#8707;<!-- &#8707; --></mi>
<mi>y</mi>
<mo>.</mo>
<mo stretchy="false">[</mo>
<mi>y</mi>
<mo>&gt;</mo>
<mi>x</mi>
<mtext>&#160;AND&#160;</mtext>
<mi mathvariant="normal">&#8707;<!-- &#8707; --></mi>
<mi>z</mi>
<mo>.</mo>
<mi>y</mi>
<mo>+</mo>
<mi>z</mi>
<mo>=</mo>
<mn>100</mn>
<mo stretchy="false">]</mo>
</math>
</label>
</div>
<span id="answer_c70ffbdf44f04efdbdf3f5310beec8a3_3_1"/>
</fieldset>
<div class="indicator-container">
<span class="status unanswered" id="status_c70ffbdf44f04efdbdf3f5310beec8a3_3_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
</div>
</div></div>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 3" role="group"><p> 3. The real numbers </p>
<div class="choicegroup capa_inputtype" id="inputtype_c70ffbdf44f04efdbdf3f5310beec8a3_4_1">
<fieldset aria-describedby="status_c70ffbdf44f04efdbdf3f5310beec8a3_4_1">
<div class="field">
<input type="checkbox" name="input_c70ffbdf44f04efdbdf3f5310beec8a3_4_1[]" id="input_c70ffbdf44f04efdbdf3f5310beec8a3_4_1_choice_0" class="field-input input-checkbox" value="choice_0"/><label id="c70ffbdf44f04efdbdf3f5310beec8a3_4_1-choice_0-label" for="input_c70ffbdf44f04efdbdf3f5310beec8a3_4_1_choice_0" class="response-label field-label label-inline" aria-describedby="status_c70ffbdf44f04efdbdf3f5310beec8a3_4_1"> <math xmlns="http://www.w3.org/1998/Math/MathML">
<mi mathvariant="normal">&#8704;<!-- &#8704; --></mi>
<mi>x</mi>
<mi mathvariant="normal">&#8707;<!-- &#8707; --></mi>
<mi>y</mi>
<mo>.</mo>
<mn>2</mn>
<mi>x</mi>
<mo>&#8722;<!-- &#8722; --></mo>
<mi>y</mi>
<mo>=</mo>
<mn>0</mn>
</math>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_c70ffbdf44f04efdbdf3f5310beec8a3_4_1[]" id="input_c70ffbdf44f04efdbdf3f5310beec8a3_4_1_choice_1" class="field-input input-checkbox" value="choice_1"/><label id="c70ffbdf44f04efdbdf3f5310beec8a3_4_1-choice_1-label" for="input_c70ffbdf44f04efdbdf3f5310beec8a3_4_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_c70ffbdf44f04efdbdf3f5310beec8a3_4_1"> <math xmlns="http://www.w3.org/1998/Math/MathML">
<mi mathvariant="normal">&#8704;<!-- &#8704; --></mi>
<mi>x</mi>
<mi mathvariant="normal">&#8707;<!-- &#8707; --></mi>
<mi>y</mi>
<mo>.</mo>
<mi>x</mi>
<mo>&#8722;<!-- &#8722; --></mo>
<mn>2</mn>
<mi>y</mi>
<mo>=</mo>
<mn>0</mn>
</math>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_c70ffbdf44f04efdbdf3f5310beec8a3_4_1[]" id="input_c70ffbdf44f04efdbdf3f5310beec8a3_4_1_choice_2" class="field-input input-checkbox" value="choice_2"/><label id="c70ffbdf44f04efdbdf3f5310beec8a3_4_1-choice_2-label" for="input_c70ffbdf44f04efdbdf3f5310beec8a3_4_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_c70ffbdf44f04efdbdf3f5310beec8a3_4_1"> <math xmlns="http://www.w3.org/1998/Math/MathML">
<mi mathvariant="normal">&#8704;<!-- &#8704; --></mi>
<mi>x</mi>
<mo>.</mo>
<mi>x</mi>
<mo>&lt;</mo>
<mn>10</mn>
<mtext>&#160;IMPLIES&#160;</mtext>
<mo stretchy="false">[</mo>
<mi mathvariant="normal">&#8704;<!-- &#8704; --></mi>
<mi>y</mi>
<mo>.</mo>
<mi>y</mi>
<mo>&lt;</mo>
<mi>x</mi>
<mtext>&#160;IMPLIES&#160;</mtext>
<mi>y</mi>
<mo>&lt;</mo>
<mn>9</mn>
<mo stretchy="false">]</mo>
</math>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_c70ffbdf44f04efdbdf3f5310beec8a3_4_1[]" id="input_c70ffbdf44f04efdbdf3f5310beec8a3_4_1_choice_3" class="field-input input-checkbox" value="choice_3"/><label id="c70ffbdf44f04efdbdf3f5310beec8a3_4_1-choice_3-label" for="input_c70ffbdf44f04efdbdf3f5310beec8a3_4_1_choice_3" class="response-label field-label label-inline" aria-describedby="status_c70ffbdf44f04efdbdf3f5310beec8a3_4_1"> <math xmlns="http://www.w3.org/1998/Math/MathML">
<mi mathvariant="normal">&#8704;<!-- &#8704; --></mi>
<mi>x</mi>
<mi mathvariant="normal">&#8707;<!-- &#8707; --></mi>
<mi>y</mi>
<mo>.</mo>
<mo stretchy="false">[</mo>
<mi>y</mi>
<mo>&gt;</mo>
<mi>x</mi>
<mtext>&#160;AND&#160;</mtext>
<mi mathvariant="normal">&#8707;<!-- &#8707; --></mi>
<mi>z</mi>
<mo>.</mo>
<mi>y</mi>
<mo>+</mo>
<mi>z</mi>
<mo>=</mo>
<mn>100</mn>
<mo stretchy="false">]</mo>
</math>
</label>
</div>
<span id="answer_c70ffbdf44f04efdbdf3f5310beec8a3_4_1"/>
</fieldset>
<div class="indicator-container">
<span class="status unanswered" id="status_c70ffbdf44f04efdbdf3f5310beec8a3_4_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
</div>
</div></div>
<div class="solution-span">
<span id="solution_c70ffbdf44f04efdbdf3f5310beec8a3_solution_1"/>
</div><div class="solution-span">
<span id="solution_c70ffbdf44f04efdbdf3f5310beec8a3_solution_2"/>
</div></div>
<div class="action">
<input type="hidden" name="problem_id" value="Propositions with Quantifiers" />
<div class="submit-attempt-container">
<button type="button" class="submit btn-brand" data-submitting="Submitting" data-value="Submit" data-should-enable-submit-button="True" aria-describedby="submission_feedback_c70ffbdf44f04efdbdf3f5310beec8a3" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_c70ffbdf44f04efdbdf3f5310beec8a3">
<span class="sr">Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.</span>
</div>
</div>
<div class="problem-action-buttons-wrapper">
<span class="problem-action-button-wrapper">
<button type="button" class="reset problem-action-btn btn-default btn-small" data-value="Reset"><span class="icon fa fa-refresh" aria-hidden="true"></span><span aria-hidden="true">Reset</span><span class="sr">Reset your answer</span></button>
</span>
<span class="problem-action-button-wrapper">
<button type="button" class="show problem-action-btn btn-default btn-small" aria-describedby="c70ffbdf44f04efdbdf3f5310beec8a3-problem-title"><span class="icon fa fa-info-circle" aria-hidden="true"></span><span class="show-label">Show Answer</span></button>
</span>
</div>
</div>
<div class="notification warning notification-gentle-alert
is-hidden"
tabindex="-1">
<span class="icon fa fa-exclamation-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="c70ffbdf44f04efdbdf3f5310beec8a3-problem-title">
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification warning notification-save
is-hidden"
tabindex="-1">
<span class="icon fa fa-save" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="c70ffbdf44f04efdbdf3f5310beec8a3-problem-title">None
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification general notification-show-answer
is-hidden"
tabindex="-1">
<span class="icon fa fa-info-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="c70ffbdf44f04efdbdf3f5310beec8a3-problem-title">Answers are displayed within the problem
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
</div>
"
data-graded="False">
<p class="loading-spinner">
<i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i>
<span class="sr">Loading…</span>
</p>
</div>
</div>
</div>
</div>
</div>
<div class="xblock xblock-public_view xblock-public_view-vertical" data-block-type="vertical" data-runtime-version="1" data-usage-id="block-v1:OCW+6.042J+2T2019+type@vertical+block@331365094d464345acf96f210604f7cf" data-graded="False" data-runtime-class="LmsRuntime" data-course-id="course-v1:OCW+6.042J+2T2019" data-has-score="False" data-init="VerticalStudentView" data-request-token="7ec97d12dbd311efb03c029b57e3cc89">
<h2 class="hd hd-2 unit-title">Exercise | Predicate Logic</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:OCW+6.042J+2T2019+type@problem+block@3354dc320738455c8842448b4a897ac0">
<div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-block-type="problem" data-runtime-version="1" data-usage-id="block-v1:OCW+6.042J+2T2019+type@problem+block@3354dc320738455c8842448b4a897ac0" data-graded="False" data-runtime-class="LmsRuntime" data-course-id="course-v1:OCW+6.042J+2T2019" data-has-score="True" data-init="XBlockToXModuleShim" data-request-token="7ec97d12dbd311efb03c029b57e3cc89">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Problem"}
</script>
<div id="problem_3354dc320738455c8842448b4a897ac0" class="problems-wrapper" role="group"
aria-labelledby="3354dc320738455c8842448b4a897ac0-problem-title"
data-problem-id="block-v1:OCW+6.042J+2T2019+type@problem+block@3354dc320738455c8842448b4a897ac0" data-url="/courses/course-v1:OCW+6.042J+2T2019/xblock/block-v1:OCW+6.042J+2T2019+type@problem+block@3354dc320738455c8842448b4a897ac0/handler/xmodule_handler"
data-problem-score="0"
data-problem-total-possible="1"
data-attempts-used="0"
data-content="
<h3 class="hd hd-3 problem-header" id="3354dc320738455c8842448b4a897ac0-problem-title" aria-describedby="block-v1:OCW+6.042J+2T2019+type@problem+block@3354dc320738455c8842448b4a897ac0-problem-progress" tabindex="-1">
Predicate Logic
</h3>
<div class="problem-progress" id="block-v1:OCW+6.042J+2T2019+type@problem+block@3354dc320738455c8842448b4a897ac0-problem-progress"></div>
<div class="problem">
<div>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div class="choicegroup capa_inputtype" id="inputtype_3354dc320738455c8842448b4a897ac0_2_1">
<fieldset aria-describedby="status_3354dc320738455c8842448b4a897ac0_2_1">
<legend id="3354dc320738455c8842448b4a897ac0_2_1-legend" class="response-fieldset-legend field-group-hd">Which of the following are <em>valid</em>?</legend>
<div class="field">
<input type="checkbox" name="input_3354dc320738455c8842448b4a897ac0_2_1[]" id="input_3354dc320738455c8842448b4a897ac0_2_1_choice_0" class="field-input input-checkbox" value="choice_0"/><label id="3354dc320738455c8842448b4a897ac0_2_1-choice_0-label" for="input_3354dc320738455c8842448b4a897ac0_2_1_choice_0" class="response-label field-label label-inline" aria-describedby="status_3354dc320738455c8842448b4a897ac0_2_1"> <math xmlns="http://www.w3.org/1998/Math/MathML">
<mi mathvariant="normal">&#8707;<!-- &#8707; --></mi>
<mi>x</mi>
<mi mathvariant="normal">&#8707;<!-- &#8707; --></mi>
<mi>y</mi>
<mo>.</mo>
<mi>P</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo>,</mo>
<mi>y</mi>
<mo stretchy="false">)</mo>
<mtext>&#160;IMPLIES&#160;</mtext>
<mi mathvariant="normal">&#8707;<!-- &#8707; --></mi>
<mi>y</mi>
<mi mathvariant="normal">&#8707;<!-- &#8707; --></mi>
<mi>x</mi>
<mo>.</mo>
<mi>P</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo>,</mo>
<mi>y</mi>
<mo stretchy="false">)</mo>
</math>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_3354dc320738455c8842448b4a897ac0_2_1[]" id="input_3354dc320738455c8842448b4a897ac0_2_1_choice_1" class="field-input input-checkbox" value="choice_1"/><label id="3354dc320738455c8842448b4a897ac0_2_1-choice_1-label" for="input_3354dc320738455c8842448b4a897ac0_2_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_3354dc320738455c8842448b4a897ac0_2_1"> <math xmlns="http://www.w3.org/1998/Math/MathML">
<mi mathvariant="normal">&#8704;<!-- &#8704; --></mi>
<mi>x</mi>
<mi mathvariant="normal">&#8707;<!-- &#8707; --></mi>
<mi>y</mi>
<mo>.</mo>
<mi>Q</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo>,</mo>
<mi>y</mi>
<mo stretchy="false">)</mo>
<mtext>&#160;IMPLIES&#160;</mtext>
<mi mathvariant="normal">&#8707;<!-- &#8707; --></mi>
<mi>y</mi>
<mi mathvariant="normal">&#8704;<!-- &#8704; --></mi>
<mi>x</mi>
<mo>.</mo>
<mi>Q</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo>,</mo>
<mi>y</mi>
<mo stretchy="false">)</mo>
</math>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_3354dc320738455c8842448b4a897ac0_2_1[]" id="input_3354dc320738455c8842448b4a897ac0_2_1_choice_2" class="field-input input-checkbox" value="choice_2"/><label id="3354dc320738455c8842448b4a897ac0_2_1-choice_2-label" for="input_3354dc320738455c8842448b4a897ac0_2_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_3354dc320738455c8842448b4a897ac0_2_1"> <math xmlns="http://www.w3.org/1998/Math/MathML">
<mi mathvariant="normal">&#8707;<!-- &#8707; --></mi>
<mi>x</mi>
<mi mathvariant="normal">&#8704;<!-- &#8704; --></mi>
<mi>y</mi>
<mo>.</mo>
<mi>R</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo>,</mo>
<mi>y</mi>
<mo stretchy="false">)</mo>
<mtext>&#160;IMPLIES&#160;</mtext>
<mi mathvariant="normal">&#8704;<!-- &#8704; --></mi>
<mi>y</mi>
<mi mathvariant="normal">&#8707;<!-- &#8707; --></mi>
<mi>x</mi>
<mo>.</mo>
<mi>R</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo>,</mo>
<mi>y</mi>
<mo stretchy="false">)</mo>
</math>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_3354dc320738455c8842448b4a897ac0_2_1[]" id="input_3354dc320738455c8842448b4a897ac0_2_1_choice_3" class="field-input input-checkbox" value="choice_3"/><label id="3354dc320738455c8842448b4a897ac0_2_1-choice_3-label" for="input_3354dc320738455c8842448b4a897ac0_2_1_choice_3" class="response-label field-label label-inline" aria-describedby="status_3354dc320738455c8842448b4a897ac0_2_1"> <math xmlns="http://www.w3.org/1998/Math/MathML">
<mtext>NOT</mtext>
<mo stretchy="false">[</mo>
<mi mathvariant="normal">&#8707;<!-- &#8707; --></mi>
<mi>x</mi>
<mo>.</mo>
<mi>S</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo stretchy="false">]</mo>
<mtext>&#160;IFF&#160;</mtext>
<mi mathvariant="normal">&#8704;<!-- &#8704; --></mi>
<mi>x</mi>
<mo>.</mo>
<mtext>NOT</mtext>
<mo stretchy="false">[</mo>
<mi>S</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo stretchy="false">]</mo>
</math>
</label>
</div>
<span id="answer_3354dc320738455c8842448b4a897ac0_2_1"/>
</fieldset>
<div class="indicator-container">
<span class="status unanswered" id="status_3354dc320738455c8842448b4a897ac0_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
</div>
</div><div class="solution-span">
<span id="solution_3354dc320738455c8842448b4a897ac0_solution_1"/>
</div></div>
</div>
<div class="action">
<input type="hidden" name="problem_id" value="Predicate Logic" />
<div class="submit-attempt-container">
<button type="button" class="submit btn-brand" data-submitting="Submitting" data-value="Submit" data-should-enable-submit-button="True" aria-describedby="submission_feedback_3354dc320738455c8842448b4a897ac0" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_3354dc320738455c8842448b4a897ac0">
<span class="sr">Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.</span>
</div>
</div>
<div class="problem-action-buttons-wrapper">
<span class="problem-action-button-wrapper">
<button type="button" class="reset problem-action-btn btn-default btn-small" data-value="Reset"><span class="icon fa fa-refresh" aria-hidden="true"></span><span aria-hidden="true">Reset</span><span class="sr">Reset your answer</span></button>
</span>
<span class="problem-action-button-wrapper">
<button type="button" class="show problem-action-btn btn-default btn-small" aria-describedby="3354dc320738455c8842448b4a897ac0-problem-title"><span class="icon fa fa-info-circle" aria-hidden="true"></span><span class="show-label">Show Answer</span></button>
</span>
</div>
</div>
<div class="notification warning notification-gentle-alert
is-hidden"
tabindex="-1">
<span class="icon fa fa-exclamation-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="3354dc320738455c8842448b4a897ac0-problem-title">
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification warning notification-save
is-hidden"
tabindex="-1">
<span class="icon fa fa-save" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="3354dc320738455c8842448b4a897ac0-problem-title">None
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification general notification-show-answer
is-hidden"
tabindex="-1">
<span class="icon fa fa-info-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="3354dc320738455c8842448b4a897ac0-problem-title">Answers are displayed within the problem
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
</div>
"
data-graded="False">
<p class="loading-spinner">
<i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i>
<span class="sr">Loading…</span>
</p>
</div>
</div>
</div>
</div>
</div>