CS2022oldt1 - a) If 1 + 1 = 2 then 2 +2 = 4 b) 1 + 1 = 3...

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Name_________________ CS2022 Test #1 Friday, November 5, 2004 150 Points #1. (30 points) Let h = “John is healthy” w = “John is wealthy” s = “John is wise” Write statements in symbolic form using h, w, and s and the appropriate logical connectives for each of the following: a) John is healthy, wealthy, but not wise. b) John is neither wealthy nor wise, but he is healthy. c) John is wealthy, but he is not both healthy and wise. 2. (20 points) Let R(x): “x is a rational number” I(x): “x is an integer” Express “All integers are rational numbers, but some rational numbers are not integers” using R(x), I(x), quantifiers and logical connectives. #3. (20 points) Which of the following implications are true? Justify your answer.
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Unformatted text preview: a) If 1 + 1 = 2 then 2 +2 = 4 b) 1 + 1 = 3 only if 2 + 2 = 6 #4. (60 points) Determine whether each of the following statements is true or false. Justify your answer with a proof or counterexample, as appropriate. Be clear! a) The product of any two odd integers, x and y , is odd b) The difference of any two odd integers, x and y , is odd c) For all integers n , 4(n 2 + n + 1) 3n 2 is a perfect square 5. (20 points) Using a symbolic derivation, show: 5. (20 points) Using a symbolic derivation, show: ( p p q ) ) ( ( p r ) p p q r . Here is the first step: Step Reasons ( ( p p q ) ) ( ( p r ) ( p q ) ( p r ) a b = ~a v b...
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This note was uploaded on 06/12/2011 for the course MATH 103 taught by Professor Wouters during the Spring '08 term at Wisc Oshkosh.

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CS2022oldt1 - a) If 1 + 1 = 2 then 2 +2 = 4 b) 1 + 1 = 3...

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