Quiz 01 Solutions

# Quiz 01 Solutions - MATH 74 QUIZ 1 February 6th 2009 Name...

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MATH 74 QUIZ 1 February 6th, 2009 Name: Show all work and attempt to write neatly. There is a total of 60 points. 1. (10 points) Let A,B be subsets of U . Prove that A S B = ( A T B c ) S B . We have ( A ± B c ) [ B = { x U | ( x A x B c ) x B } = { x U | ( x A x / B ) x B } = { x U | ( x A x B ) ( x B x / B ) } where the second line follows from the distributive property of and . But x B x / B is equivalent to x U , which is always true. Thus we ﬁnd ( A ± B c ) [ B = { x U | ( x A x B ) ( x U } = { x U | x A x B } = A [ B. 2. (10 points) Let P,Q,R be propositions. Let A be the proposition P = (( Q = R ) and ( R = Q )) . Let B be the proposition (not P and ( Q or R )) or ( P and ( Q and R )) . Use truth tables to decide whether or not A and B are logically equivalent. If

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Quiz 01 Solutions - MATH 74 QUIZ 1 February 6th 2009 Name...

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