30+Midterm+Solutions

30+Midterm+Solutions - Handout #30 April 25, 2011 CS103...

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Handout #30 CS103 April 25, 2011 Robert Plummer CS103--Midterm Solutions 1. Propositional Logic (16 points) Give a formal proof for the following. The conclusion is written at the bottom to give you room to fill in your steps. Use numbered steps and refer to those numbers in the justification you give for each step. You will find useful tables at the end of the exam. Cite named rules, or just the table and line number if the rule is not named. 1. (¬S ¬Q) ¬W 2. P R 3. ¬W ¬R 4. P R
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2 2. Proof with Quantifiers (22 points) Give a formal proof for the following. Use numbered steps and refer to those numbers in the justification you give for each step. You will find useful tables at the end of the exam. Cite named rules, or just the table and line number if the rule is not named. As always, you may assume that the universe of discourse is not empty. 1. x ( Small(x) Cube(x) ) 2. ( x ¬Cube(x)) ( x Small(x)) Here is a proof by contradiction:
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3 Here is a proof by cases:
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4 3. Equivalences (12 points) In each part below, put a check mark beside each sentence that is equivalent to the given sentence (a) - (c). More than one may be equivalent or none may be equivalent.
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This note was uploaded on 06/01/2011 for the course EE 103 taught by Professor Plummer during the Spring '11 term at Stanford.

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30+Midterm+Solutions - Handout #30 April 25, 2011 CS103...

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