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30+Midterm+Solutions

# 30+Midterm+Solutions - Handout#30 CS103 Robert Plummer...

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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:
3 Here is a proof by cases:

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4 3. Equivalences (12 points)
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