Midterm1Sol

Midterm1Sol - CS 182 Fall 2009 Prof. Ananth Grama Name:...

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CS 182 – Fall 2009 Name: Prof. Ananth Grama MIDTERM #1 This is an open book, open notes exam. However, you are not allowed to share any material with anyone else during the exam. Any evidence of academic dishonesty will be dealt with strictly in accordance with existing rules at Purdue University. The exam consists of 7 questions on the following 7 pages. Each question is worth 10 points. Problem Maximum Score 1 10 2 10 3 10 4 10 5 10 6 10 7 10 Total 70
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a. (4 pts) Determine whether ¬ ( p ( p q )) is a tautology. Here is a solution using a truth table: p q ( p q ) ( p ( p q )) ¬ ( p ( p q )) T T T F T T F T F T F T T T F F F F F T So it is not a tautology. b. (6 pts) Determine whether ( p q ) ( q r ) and ( p r ) are logically equivalent. Here is a solution using a truth table: p q r p q q r ( p q ) ( q r ) p r T T T T T T T T T F T F F F T F T F T T T T F F F T T F F T T T T T T F T F T F T T F F T T T T T F F F T T T T So they are not logically equivalent (see p = T,q = F,r = F ). 2
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Midterm1Sol - CS 182 Fall 2009 Prof. Ananth Grama Name:...

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