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<h2 class="hd hd-2 unit-title">Introduction</h2>
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<p>Read <a href="/assets/courseware/v1/683102c815232991184d4f8f8b4856b5/asset-v1:OCW+6.042J+2T2019+type@asset+block/MIT6_042JS15_Session4.pdf" target="[object Object]">Chapter 3.1–3.5 (PDF)</a> of <em>Mathematics for Computer Science</em> for 1.4 Logic & Propositions.</p>
<p>View the <a href="/assets/courseware/v1/04fc8e89039320c0b5cfa4a974507f12/asset-v1:OCW+6.042J+2T2019+type@asset+block/MIT6_042JS15_cp4.pdf" target="[object Object]">Section 1.4 In-Class Questions (PDF)</a></p>
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<h2 class="hd hd-2 unit-title">Lecture Video | Propositional Operators</h2>
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<p>Download a copy of the slides for <a href="/assets/courseware/v1/0f29951ce4cb05bbfefd791869ab73a6/asset-v1:OCW+6.042J+2T2019+type@asset+block/MIT6_042JS16_PropositOper_Slides.pdf" target="[object Object]">Propositional Operators (PDF)</a> <br /><br /><a href="/assets/courseware/v1/7648680e3243bf0e31972e7b74fccd59/asset-v1:OCW+6.042J+2T2019+type@asset+block/Prop_Op_1.4_lectrans.pdf" target="[object Object]">Lecture video transcript (PDF)</a></p>
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<h2 class="hd hd-2 unit-title">Exercise | Propositional Operators</h2>
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Propositional Operators
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<span class="status unanswered" id="status_ae5d5609697b45c89a61e30580690a31_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
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<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 2" role="group"><div class="choicegroup capa_inputtype" id="inputtype_ae5d5609697b45c89a61e30580690a31_3_1">
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<mi>P</mi>
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<div class="field">
<input type="checkbox" name="input_ae5d5609697b45c89a61e30580690a31_3_1[]" id="input_ae5d5609697b45c89a61e30580690a31_3_1_choice_3" class="field-input input-checkbox" value="choice_3"/><label id="ae5d5609697b45c89a61e30580690a31_3_1-choice_3-label" for="input_ae5d5609697b45c89a61e30580690a31_3_1_choice_3" class="response-label field-label label-inline" aria-describedby="status_ae5d5609697b45c89a61e30580690a31_3_1"> <math xmlns="http://www.w3.org/1998/Math/MathML">
<mtext>NOT&#160;</mtext>
<mo stretchy="false">[</mo>
<mi>P</mi>
<mtext>&#160;AND&#160;</mtext>
<mi>Q</mi>
<mo stretchy="false">]</mo>
</math>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_ae5d5609697b45c89a61e30580690a31_3_1[]" id="input_ae5d5609697b45c89a61e30580690a31_3_1_choice_4" class="field-input input-checkbox" value="choice_4"/><label id="ae5d5609697b45c89a61e30580690a31_3_1-choice_4-label" for="input_ae5d5609697b45c89a61e30580690a31_3_1_choice_4" class="response-label field-label label-inline" aria-describedby="status_ae5d5609697b45c89a61e30580690a31_3_1"> <math xmlns="http://www.w3.org/1998/Math/MathML">
<mtext>NOT&#160;</mtext>
<mo stretchy="false">[</mo>
<mi>P</mi>
<mtext>&#160;OR&#160;</mtext>
<mi>Q</mi>
<mo stretchy="false">]</mo>
</math>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_ae5d5609697b45c89a61e30580690a31_3_1[]" id="input_ae5d5609697b45c89a61e30580690a31_3_1_choice_5" class="field-input input-checkbox" value="choice_5"/><label id="ae5d5609697b45c89a61e30580690a31_3_1-choice_5-label" for="input_ae5d5609697b45c89a61e30580690a31_3_1_choice_5" class="response-label field-label label-inline" aria-describedby="status_ae5d5609697b45c89a61e30580690a31_3_1"> <math xmlns="http://www.w3.org/1998/Math/MathML">
<mtext>NOT&#160;</mtext>
<mi>P</mi>
</math>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_ae5d5609697b45c89a61e30580690a31_3_1[]" id="input_ae5d5609697b45c89a61e30580690a31_3_1_choice_6" class="field-input input-checkbox" value="choice_6"/><label id="ae5d5609697b45c89a61e30580690a31_3_1-choice_6-label" for="input_ae5d5609697b45c89a61e30580690a31_3_1_choice_6" class="response-label field-label label-inline" aria-describedby="status_ae5d5609697b45c89a61e30580690a31_3_1"> <math xmlns="http://www.w3.org/1998/Math/MathML">
<mtext>NOT&#160;</mtext>
<mi>Q</mi>
</math>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_ae5d5609697b45c89a61e30580690a31_3_1[]" id="input_ae5d5609697b45c89a61e30580690a31_3_1_choice_7" class="field-input input-checkbox" value="choice_7"/><label id="ae5d5609697b45c89a61e30580690a31_3_1-choice_7-label" for="input_ae5d5609697b45c89a61e30580690a31_3_1_choice_7" class="response-label field-label label-inline" aria-describedby="status_ae5d5609697b45c89a61e30580690a31_3_1"> <math xmlns="http://www.w3.org/1998/Math/MathML">
<mtext>NOT&#160;</mtext>
<mo stretchy="false">[</mo>
<mi>P</mi>
<mo stretchy="false">]</mo>
<mtext>&#160;AND&#160;</mtext>
<mi>Q</mi>
</math>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_ae5d5609697b45c89a61e30580690a31_3_1[]" id="input_ae5d5609697b45c89a61e30580690a31_3_1_choice_8" class="field-input input-checkbox" value="choice_8"/><label id="ae5d5609697b45c89a61e30580690a31_3_1-choice_8-label" for="input_ae5d5609697b45c89a61e30580690a31_3_1_choice_8" class="response-label field-label label-inline" aria-describedby="status_ae5d5609697b45c89a61e30580690a31_3_1"> <math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>P</mi>
<mtext>&#160;OR&#160;</mtext>
<mtext>NOT&#160;</mtext>
<mi>Q</mi>
</math>
</label>
</div>
<span id="answer_ae5d5609697b45c89a61e30580690a31_3_1"/>
</fieldset>
<div class="indicator-container">
<span class="status unanswered" id="status_ae5d5609697b45c89a61e30580690a31_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"><div class="choicegroup capa_inputtype" id="inputtype_ae5d5609697b45c89a61e30580690a31_4_1">
<fieldset aria-describedby="status_ae5d5609697b45c89a61e30580690a31_4_1">
<legend id="ae5d5609697b45c89a61e30580690a31_4_1-legend" class="response-fieldset-legend field-group-hd">3. When <math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>P</mi>
</math> is true and <math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>Q</mi>
</math> is false, which of the following evaluate to true?</legend>
<div class="field">
<input type="checkbox" name="input_ae5d5609697b45c89a61e30580690a31_4_1[]" id="input_ae5d5609697b45c89a61e30580690a31_4_1_choice_0" class="field-input input-checkbox" value="choice_0"/><label id="ae5d5609697b45c89a61e30580690a31_4_1-choice_0-label" for="input_ae5d5609697b45c89a61e30580690a31_4_1_choice_0" class="response-label field-label label-inline" aria-describedby="status_ae5d5609697b45c89a61e30580690a31_4_1"> <math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>P</mi>
<mtext>&#160;XOR&#160;</mtext>
<mi>Q</mi>
</math>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_ae5d5609697b45c89a61e30580690a31_4_1[]" id="input_ae5d5609697b45c89a61e30580690a31_4_1_choice_1" class="field-input input-checkbox" value="choice_1"/><label id="ae5d5609697b45c89a61e30580690a31_4_1-choice_1-label" for="input_ae5d5609697b45c89a61e30580690a31_4_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_ae5d5609697b45c89a61e30580690a31_4_1"> <math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>P</mi>
<mtext>&#160;AND&#160;</mtext>
<mi>Q</mi>
</math>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_ae5d5609697b45c89a61e30580690a31_4_1[]" id="input_ae5d5609697b45c89a61e30580690a31_4_1_choice_2" class="field-input input-checkbox" value="choice_2"/><label id="ae5d5609697b45c89a61e30580690a31_4_1-choice_2-label" for="input_ae5d5609697b45c89a61e30580690a31_4_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_ae5d5609697b45c89a61e30580690a31_4_1"> <math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>P</mi>
<mtext>&#160;OR&#160;</mtext>
<mi>Q</mi>
</math>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_ae5d5609697b45c89a61e30580690a31_4_1[]" id="input_ae5d5609697b45c89a61e30580690a31_4_1_choice_3" class="field-input input-checkbox" value="choice_3"/><label id="ae5d5609697b45c89a61e30580690a31_4_1-choice_3-label" for="input_ae5d5609697b45c89a61e30580690a31_4_1_choice_3" class="response-label field-label label-inline" aria-describedby="status_ae5d5609697b45c89a61e30580690a31_4_1"> <math xmlns="http://www.w3.org/1998/Math/MathML">
<mtext>NOT&#160;</mtext>
<mo stretchy="false">[</mo>
<mi>P</mi>
<mtext>&#160;AND&#160;</mtext>
<mi>Q</mi>
<mo stretchy="false">]</mo>
</math>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_ae5d5609697b45c89a61e30580690a31_4_1[]" id="input_ae5d5609697b45c89a61e30580690a31_4_1_choice_4" class="field-input input-checkbox" value="choice_4"/><label id="ae5d5609697b45c89a61e30580690a31_4_1-choice_4-label" for="input_ae5d5609697b45c89a61e30580690a31_4_1_choice_4" class="response-label field-label label-inline" aria-describedby="status_ae5d5609697b45c89a61e30580690a31_4_1"> <math xmlns="http://www.w3.org/1998/Math/MathML">
<mtext>NOT&#160;</mtext>
<mo stretchy="false">[</mo>
<mi>P</mi>
<mtext>&#160;OR&#160;</mtext>
<mi>Q</mi>
<mo stretchy="false">]</mo>
</math>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_ae5d5609697b45c89a61e30580690a31_4_1[]" id="input_ae5d5609697b45c89a61e30580690a31_4_1_choice_5" class="field-input input-checkbox" value="choice_5"/><label id="ae5d5609697b45c89a61e30580690a31_4_1-choice_5-label" for="input_ae5d5609697b45c89a61e30580690a31_4_1_choice_5" class="response-label field-label label-inline" aria-describedby="status_ae5d5609697b45c89a61e30580690a31_4_1"> <math xmlns="http://www.w3.org/1998/Math/MathML">
<mtext>NOT&#160;</mtext>
<mi>P</mi>
</math>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_ae5d5609697b45c89a61e30580690a31_4_1[]" id="input_ae5d5609697b45c89a61e30580690a31_4_1_choice_6" class="field-input input-checkbox" value="choice_6"/><label id="ae5d5609697b45c89a61e30580690a31_4_1-choice_6-label" for="input_ae5d5609697b45c89a61e30580690a31_4_1_choice_6" class="response-label field-label label-inline" aria-describedby="status_ae5d5609697b45c89a61e30580690a31_4_1"> <math xmlns="http://www.w3.org/1998/Math/MathML">
<mtext>NOT&#160;</mtext>
<mi>Q</mi>
</math>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_ae5d5609697b45c89a61e30580690a31_4_1[]" id="input_ae5d5609697b45c89a61e30580690a31_4_1_choice_7" class="field-input input-checkbox" value="choice_7"/><label id="ae5d5609697b45c89a61e30580690a31_4_1-choice_7-label" for="input_ae5d5609697b45c89a61e30580690a31_4_1_choice_7" class="response-label field-label label-inline" aria-describedby="status_ae5d5609697b45c89a61e30580690a31_4_1"> <math xmlns="http://www.w3.org/1998/Math/MathML">
<mtext>NOT&#160;</mtext>
<mo stretchy="false">[</mo>
<mi>P</mi>
<mo stretchy="false">]</mo>
<mtext>&#160;AND&#160;</mtext>
<mi>Q</mi>
</math>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_ae5d5609697b45c89a61e30580690a31_4_1[]" id="input_ae5d5609697b45c89a61e30580690a31_4_1_choice_8" class="field-input input-checkbox" value="choice_8"/><label id="ae5d5609697b45c89a61e30580690a31_4_1-choice_8-label" for="input_ae5d5609697b45c89a61e30580690a31_4_1_choice_8" class="response-label field-label label-inline" aria-describedby="status_ae5d5609697b45c89a61e30580690a31_4_1"> <math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>P</mi>
<mtext>&#160;OR&#160;</mtext>
<mtext>NOT&#160;</mtext>
<mi>Q</mi>
</math>
</label>
</div>
<span id="answer_ae5d5609697b45c89a61e30580690a31_4_1"/>
</fieldset>
<div class="indicator-container">
<span class="status unanswered" id="status_ae5d5609697b45c89a61e30580690a31_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="wrapper-problem-response" tabindex="-1" aria-label="Question 4" role="group"><div class="choicegroup capa_inputtype" id="inputtype_ae5d5609697b45c89a61e30580690a31_5_1">
<fieldset aria-describedby="status_ae5d5609697b45c89a61e30580690a31_5_1">
<legend id="ae5d5609697b45c89a61e30580690a31_5_1-legend" class="response-fieldset-legend field-group-hd">4. When <math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>P</mi>
</math> is false and <math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>Q</mi>
</math> is true, which of the following evaluate to true?</legend>
<div class="field">
<input type="checkbox" name="input_ae5d5609697b45c89a61e30580690a31_5_1[]" id="input_ae5d5609697b45c89a61e30580690a31_5_1_choice_0" class="field-input input-checkbox" value="choice_0"/><label id="ae5d5609697b45c89a61e30580690a31_5_1-choice_0-label" for="input_ae5d5609697b45c89a61e30580690a31_5_1_choice_0" class="response-label field-label label-inline" aria-describedby="status_ae5d5609697b45c89a61e30580690a31_5_1"> <math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>P</mi>
<mtext>&#160;XOR&#160;</mtext>
<mi>Q</mi>
</math>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_ae5d5609697b45c89a61e30580690a31_5_1[]" id="input_ae5d5609697b45c89a61e30580690a31_5_1_choice_1" class="field-input input-checkbox" value="choice_1"/><label id="ae5d5609697b45c89a61e30580690a31_5_1-choice_1-label" for="input_ae5d5609697b45c89a61e30580690a31_5_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_ae5d5609697b45c89a61e30580690a31_5_1"> <math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>P</mi>
<mtext>&#160;AND&#160;</mtext>
<mi>Q</mi>
</math>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_ae5d5609697b45c89a61e30580690a31_5_1[]" id="input_ae5d5609697b45c89a61e30580690a31_5_1_choice_2" class="field-input input-checkbox" value="choice_2"/><label id="ae5d5609697b45c89a61e30580690a31_5_1-choice_2-label" for="input_ae5d5609697b45c89a61e30580690a31_5_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_ae5d5609697b45c89a61e30580690a31_5_1"> <math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>P</mi>
<mtext>&#160;OR&#160;</mtext>
<mi>Q</mi>
</math>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_ae5d5609697b45c89a61e30580690a31_5_1[]" id="input_ae5d5609697b45c89a61e30580690a31_5_1_choice_3" class="field-input input-checkbox" value="choice_3"/><label id="ae5d5609697b45c89a61e30580690a31_5_1-choice_3-label" for="input_ae5d5609697b45c89a61e30580690a31_5_1_choice_3" class="response-label field-label label-inline" aria-describedby="status_ae5d5609697b45c89a61e30580690a31_5_1"> <math xmlns="http://www.w3.org/1998/Math/MathML">
<mtext>NOT&#160;</mtext>
<mo stretchy="false">[</mo>
<mi>P</mi>
<mtext>&#160;AND&#160;</mtext>
<mi>Q</mi>
<mo stretchy="false">]</mo>
</math>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_ae5d5609697b45c89a61e30580690a31_5_1[]" id="input_ae5d5609697b45c89a61e30580690a31_5_1_choice_4" class="field-input input-checkbox" value="choice_4"/><label id="ae5d5609697b45c89a61e30580690a31_5_1-choice_4-label" for="input_ae5d5609697b45c89a61e30580690a31_5_1_choice_4" class="response-label field-label label-inline" aria-describedby="status_ae5d5609697b45c89a61e30580690a31_5_1"> <math xmlns="http://www.w3.org/1998/Math/MathML">
<mtext>NOT&#160;</mtext>
<mo stretchy="false">[</mo>
<mi>P</mi>
<mtext>&#160;OR&#160;</mtext>
<mi>Q</mi>
<mo stretchy="false">]</mo>
</math>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_ae5d5609697b45c89a61e30580690a31_5_1[]" id="input_ae5d5609697b45c89a61e30580690a31_5_1_choice_5" class="field-input input-checkbox" value="choice_5"/><label id="ae5d5609697b45c89a61e30580690a31_5_1-choice_5-label" for="input_ae5d5609697b45c89a61e30580690a31_5_1_choice_5" class="response-label field-label label-inline" aria-describedby="status_ae5d5609697b45c89a61e30580690a31_5_1"> <math xmlns="http://www.w3.org/1998/Math/MathML">
<mtext>NOT&#160;</mtext>
<mi>P</mi>
</math>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_ae5d5609697b45c89a61e30580690a31_5_1[]" id="input_ae5d5609697b45c89a61e30580690a31_5_1_choice_6" class="field-input input-checkbox" value="choice_6"/><label id="ae5d5609697b45c89a61e30580690a31_5_1-choice_6-label" for="input_ae5d5609697b45c89a61e30580690a31_5_1_choice_6" class="response-label field-label label-inline" aria-describedby="status_ae5d5609697b45c89a61e30580690a31_5_1"> <math xmlns="http://www.w3.org/1998/Math/MathML">
<mtext>NOT&#160;</mtext>
<mi>Q</mi>
</math>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_ae5d5609697b45c89a61e30580690a31_5_1[]" id="input_ae5d5609697b45c89a61e30580690a31_5_1_choice_7" class="field-input input-checkbox" value="choice_7"/><label id="ae5d5609697b45c89a61e30580690a31_5_1-choice_7-label" for="input_ae5d5609697b45c89a61e30580690a31_5_1_choice_7" class="response-label field-label label-inline" aria-describedby="status_ae5d5609697b45c89a61e30580690a31_5_1"> <math xmlns="http://www.w3.org/1998/Math/MathML">
<mtext>NOT&#160;</mtext>
<mo stretchy="false">[</mo>
<mi>P</mi>
<mo stretchy="false">]</mo>
<mtext>&#160;AND&#160;</mtext>
<mi>Q</mi>
</math>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_ae5d5609697b45c89a61e30580690a31_5_1[]" id="input_ae5d5609697b45c89a61e30580690a31_5_1_choice_8" class="field-input input-checkbox" value="choice_8"/><label id="ae5d5609697b45c89a61e30580690a31_5_1-choice_8-label" for="input_ae5d5609697b45c89a61e30580690a31_5_1_choice_8" class="response-label field-label label-inline" aria-describedby="status_ae5d5609697b45c89a61e30580690a31_5_1"> <math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>P</mi>
<mtext>&#160;OR&#160;</mtext>
<mtext>NOT&#160;</mtext>
<mi>Q</mi>
</math>
</label>
</div>
<span id="answer_ae5d5609697b45c89a61e30580690a31_5_1"/>
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<h2 class="hd hd-2 unit-title">Lecture Video | Digital Logic</h2>
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<h2 class="hd hd-2 unit-title">Exercise | Equivalence and Truth Table</h2>
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Equivalence and Truth Table
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<h2 class="hd hd-2 unit-title">Slide Lecture | Implies</h2>
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<h2 class="hd hd-2 unit-title">Slide Lecture | Propositional Logic</h2>
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<h2 class="hd hd-2 unit-title">Exercise | Soundness and Validity</h2>
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Soundness and Validity
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<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><p>A rule is _____ <ns0:math xmlns:ns0="http://www.w3.org/1998/Math/MathML">
<ns0:mtext>&#160;IFF&#160;</ns0:mtext>
</ns0:math> an assignment of truth values that makes all antecedents true <ns0:math xmlns:ns0="http://www.w3.org/1998/Math/MathML">
<ns0:mtext>&#160;IMPLIES&#160;</ns0:mtext>
</ns0:math> the consequent is _____.</p>
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<h2 class="hd hd-2 unit-title">Exercise | Logical Connectives</h2>
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Question 1
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<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><p>1. For each of the following formulas, choose the <ns0:math xmlns:ns0="http://www.w3.org/1998/Math/MathML">
<ns0:mrow class="MJX-TeXAtom-ORD">
<ns0:mtext>AND</ns0:mtext>
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</ns0:math>,<ns0:math xmlns:ns0="http://www.w3.org/1998/Math/MathML">
<ns0:mrow class="MJX-TeXAtom-ORD">
<ns0:mtext>OR</ns0:mtext>
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Question 2
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Question 3
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