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<h2 class="hd hd-2 unit-title">Introduction</h2>
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<p style="font-size: 16px;">Read <a href="/assets/courseware/v1/1055804c060a43405929088b4fbce214/asset-v1:OCW+6.042J+2T2019+type@asset+block/MIT6_042JS15_Session1.pdf" target="[object Object]">Chapter 1.1–1.6 (PDF)</a> of <em>Mathematics for Computer Science</em> for 1.1 Introduction to Proofs.</p>
<p style="font-size: 16px;">View the <a href="/assets/courseware/v1/c49ce7ef21147a1ef2c3f44473bc5250/asset-v1:OCW+6.042J+2T2019+type@asset+block/MIT6_042JS15_cp1.pdf" target="[object Object]">Section 1.1 In-Class Questions (PDF)</a></p>
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<h2 class="hd hd-2 unit-title">Lecture Video | Intro to Proofs Part 1</h2>
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<p>Download a copy of the slides for <a href="/assets/courseware/v1/df7263a91749d95c94a2272475a56f7a/asset-v1:OCW+6.042J+2T2019+type@asset+block/MIT6_042JS16_Introduction.pdf" target="[object Object]">Intro to Proofs Part 1 (PDF)</a></p>
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<h2 class="hd hd-2 unit-title">Lecture Video | Intro to Proofs Part 2</h2>
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<h2 class="hd hd-2 unit-title">Exercise | Definitions to Know for Proofs</h2>
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Definitions to Know for Proofs
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<p>Match the definition with the concept. Use each option at most once!</p>
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<label class="problem-group-label" for="input_2834af8c488644539f9a560f32e167d4_2_1" id="label_2834af8c488644539f9a560f32e167d4_2_1">1. A statement that is either true or false:</label>
<select name="input_2834af8c488644539f9a560f32e167d4_2_1" id="input_2834af8c488644539f9a560f32e167d4_2_1" aria-describedby="status_2834af8c488644539f9a560f32e167d4_2_1">
<option value="option_2834af8c488644539f9a560f32e167d4_2_1_dummy_default">Select an option</option>
<option value="proposition"> proposition</option>
<option value="axiom"> axiom</option>
<option value="corollary"> corollary</option>
<option value="proof"> proof</option>
<option value="theorem"> theorem</option>
<option value="lemma"> lemma</option>
<option value="predicate"> predicate</option>
<option value="none of the above"> none of the above</option>
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<label class="problem-group-label" for="input_2834af8c488644539f9a560f32e167d4_3_1" id="label_2834af8c488644539f9a560f32e167d4_3_1">2. A proposition whose truth depends on the value of one or more variables:</label>
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<option value="option_2834af8c488644539f9a560f32e167d4_3_1_dummy_default">Select an option</option>
<option value="proposition"> proposition</option>
<option value="axiom"> axiom</option>
<option value="corollary"> corollary</option>
<option value="proof"> proof</option>
<option value="theorem"> theorem</option>
<option value="lemma"> lemma</option>
<option value="predicate"> predicate</option>
<option value="none of the above"> none of the above</option>
</select>
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<label class="problem-group-label" for="input_2834af8c488644539f9a560f32e167d4_4_1" id="label_2834af8c488644539f9a560f32e167d4_4_1">3. A proposition that is simply accepted as true:</label>
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<label class="problem-group-label" for="input_2834af8c488644539f9a560f32e167d4_5_1" id="label_2834af8c488644539f9a560f32e167d4_5_1">4. A sequence of logical deductions from axioms and previously proved statements that concludes with the proposition in question:</label>
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<label class="problem-group-label" for="input_2834af8c488644539f9a560f32e167d4_6_1" id="label_2834af8c488644539f9a560f32e167d4_6_1">5. An important true proposition:</label>
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<label class="problem-group-label" for="input_2834af8c488644539f9a560f32e167d4_7_1" id="label_2834af8c488644539f9a560f32e167d4_7_1">6. A preliminary proposition useful for proving later propositions:</label>
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<label class="problem-group-label" for="input_2834af8c488644539f9a560f32e167d4_8_1" id="label_2834af8c488644539f9a560f32e167d4_8_1">7. A proposition that follows in just a few logical steps from a theorem:</label>
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<h2 class="hd hd-2 unit-title">Exercise | Modus Ponens</h2>
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Modus Ponens
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<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><p>Let \(P\) be a proposition, \(Q\) be another proposition.</p>
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<legend id="83d8b073931e4262a1c8a98c02732f4d_2_1-legend" class="response-fieldset-legend field-group-hd">1. What is a proposition of the form \(\text{IF } P, \text{ THEN } Q \) called?</legend>
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<input type="radio" name="input_83d8b073931e4262a1c8a98c02732f4d_2_1" id="input_83d8b073931e4262a1c8a98c02732f4d_2_1_choice_1" class="field-input input-radio" value="choice_1"/><label id="83d8b073931e4262a1c8a98c02732f4d_2_1-choice_1-label" for="input_83d8b073931e4262a1c8a98c02732f4d_2_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_83d8b073931e4262a1c8a98c02732f4d_2_1"> if and only if
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</label>
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<input type="radio" name="input_83d8b073931e4262a1c8a98c02732f4d_2_1" id="input_83d8b073931e4262a1c8a98c02732f4d_2_1_choice_4" class="field-input input-radio" value="choice_4"/><label id="83d8b073931e4262a1c8a98c02732f4d_2_1-choice_4-label" for="input_83d8b073931e4262a1c8a98c02732f4d_2_1_choice_4" class="response-label field-label label-inline" aria-describedby="status_83d8b073931e4262a1c8a98c02732f4d_2_1"> none of the above
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<p>2. A fundamental inference rule says: \(\dfrac{P,\;\; P \text{ IMPLIES } Q}{Q}\). </p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 2" role="group"><div class="choicegroup capa_inputtype" id="inputtype_83d8b073931e4262a1c8a98c02732f4d_3_1">
<fieldset aria-describedby="status_83d8b073931e4262a1c8a98c02732f4d_3_1">
<legend id="83d8b073931e4262a1c8a98c02732f4d_3_1-legend" class="response-fieldset-legend field-group-hd">a. What is this inference rule called?</legend>
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<input type="radio" name="input_83d8b073931e4262a1c8a98c02732f4d_3_1" id="input_83d8b073931e4262a1c8a98c02732f4d_3_1_choice_0" class="field-input input-radio" value="choice_0"/><label id="83d8b073931e4262a1c8a98c02732f4d_3_1-choice_0-label" for="input_83d8b073931e4262a1c8a98c02732f4d_3_1_choice_0" class="response-label field-label label-inline" aria-describedby="status_83d8b073931e4262a1c8a98c02732f4d_3_1"> The Fundamental Inference Rule
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<div class="field">
<input type="radio" name="input_83d8b073931e4262a1c8a98c02732f4d_3_1" id="input_83d8b073931e4262a1c8a98c02732f4d_3_1_choice_1" class="field-input input-radio" value="choice_1"/><label id="83d8b073931e4262a1c8a98c02732f4d_3_1-choice_1-label" for="input_83d8b073931e4262a1c8a98c02732f4d_3_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_83d8b073931e4262a1c8a98c02732f4d_3_1"> Modus Ponens
</label>
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<input type="radio" name="input_83d8b073931e4262a1c8a98c02732f4d_3_1" id="input_83d8b073931e4262a1c8a98c02732f4d_3_1_choice_2" class="field-input input-radio" value="choice_2"/><label id="83d8b073931e4262a1c8a98c02732f4d_3_1-choice_2-label" for="input_83d8b073931e4262a1c8a98c02732f4d_3_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_83d8b073931e4262a1c8a98c02732f4d_3_1"> The Fundamental Rule of Logic
</label>
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<input type="radio" name="input_83d8b073931e4262a1c8a98c02732f4d_3_1" id="input_83d8b073931e4262a1c8a98c02732f4d_3_1_choice_3" class="field-input input-radio" value="choice_3"/><label id="83d8b073931e4262a1c8a98c02732f4d_3_1-choice_3-label" for="input_83d8b073931e4262a1c8a98c02732f4d_3_1_choice_3" class="response-label field-label label-inline" aria-describedby="status_83d8b073931e4262a1c8a98c02732f4d_3_1"> None of the above
</label>
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<span id="answer_83d8b073931e4262a1c8a98c02732f4d_3_1"/>
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<fieldset aria-describedby="status_83d8b073931e4262a1c8a98c02732f4d_4_1">
<legend id="83d8b073931e4262a1c8a98c02732f4d_4_1-legend" class="response-fieldset-legend field-group-hd">b. What is the statement above the line called?</legend>
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</label>
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<input type="radio" name="input_83d8b073931e4262a1c8a98c02732f4d_4_1" id="input_83d8b073931e4262a1c8a98c02732f4d_4_1_choice_1" class="field-input input-radio" value="choice_1"/><label id="83d8b073931e4262a1c8a98c02732f4d_4_1-choice_1-label" for="input_83d8b073931e4262a1c8a98c02732f4d_4_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_83d8b073931e4262a1c8a98c02732f4d_4_1"> antecedent
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<input type="radio" name="input_83d8b073931e4262a1c8a98c02732f4d_4_1" id="input_83d8b073931e4262a1c8a98c02732f4d_4_1_choice_2" class="field-input input-radio" value="choice_2"/><label id="83d8b073931e4262a1c8a98c02732f4d_4_1-choice_2-label" for="input_83d8b073931e4262a1c8a98c02732f4d_4_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_83d8b073931e4262a1c8a98c02732f4d_4_1"> all of the above
</label>
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<input type="radio" name="input_83d8b073931e4262a1c8a98c02732f4d_4_1" id="input_83d8b073931e4262a1c8a98c02732f4d_4_1_choice_3" class="field-input input-radio" value="choice_3"/><label id="83d8b073931e4262a1c8a98c02732f4d_4_1-choice_3-label" for="input_83d8b073931e4262a1c8a98c02732f4d_4_1_choice_3" class="response-label field-label label-inline" aria-describedby="status_83d8b073931e4262a1c8a98c02732f4d_4_1"> none of the above
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<legend id="83d8b073931e4262a1c8a98c02732f4d_5_1-legend" class="response-fieldset-legend field-group-hd">c. What is the statement below the line called?</legend>
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<legend id="83d8b073931e4262a1c8a98c02732f4d_6_1-legend" class="response-fieldset-legend field-group-hd">3. Proving a proposition's contrapositive is as good as (and sometimes easier than) proving the proposition itself. Which of the following is logically equivalent to the contrapositive of \(P \text{ IMPLIES } Q\)?</legend>
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<input type="radio" name="input_83d8b073931e4262a1c8a98c02732f4d_6_1" id="input_83d8b073931e4262a1c8a98c02732f4d_6_1_choice_0" class="field-input input-radio" value="choice_0"/><label id="83d8b073931e4262a1c8a98c02732f4d_6_1-choice_0-label" for="input_83d8b073931e4262a1c8a98c02732f4d_6_1_choice_0" class="response-label field-label label-inline" aria-describedby="status_83d8b073931e4262a1c8a98c02732f4d_6_1"> NOT(P IMPLIES Q)
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<legend id="83d8b073931e4262a1c8a98c02732f4d_7_1-legend" class="response-fieldset-legend field-group-hd">4. At the end of a proof, it is customary to write down either the delimiter _____ or the symbol _____.</legend>
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