COT3100exam1sol - 1) (8 pts) Fill in the truth table below...

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1) (8 pts) Fill in the truth table below to show that (p q) ((r ¬ q) (q ¬ p)) is not equivalent to r. p q r p q r ¬ q q ¬ p (p q) ((r ¬ q) (q ¬ p)) 0 0 0 0 1 0 0 0 0 1 0 1 0 0 0 1 0 1 0 1 1 0 1 1 1 1 1 1 1 0 0 1 1 0 1 1 0 1 1 1 0 1 1 1 0 1 0 0 0 1 1 1 1 1 0 1 List of truth assignments for which the two expressions are not logically equivalent. (Note: You may not use all of the blanks provided.) p = 0 q = 0 r = 1 p = 0 q = 1 r = 0 p = 1 q = 0 r = 0 2) (6 pts) True or False, circle the correct answer, no partial credit on this one. a) ((p q) (s t)) s t ¬ p ¬ q FALSE False, De Morgan’s was applied incorrectly. b) (p q) (q r) is a tautology. TRUE This is always true, because q will always imply q or r. c) ( ¬ (p q) p) p FALSE When p=q=1 both sides are not equal.
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3) (10 pts) Here are several arguments. Some are valid and some are not. For the valid ones, circle “VALID” and state the rule of inference used. For the invalid ones, simply circle “INVALID”. a) Today, I will either do my homework or call my friend Jennifer. I did not do my homework. Therefore, I did call Jennifer today. VALID
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COT3100exam1sol - 1) (8 pts) Fill in the truth table below...

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