e211k - MAD 2104 Quiz 2 and Key Prof S Hudson 1[20pts List...

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MAD 2104 Sept 15, 2011 Quiz 2 and Key Prof. S. Hudson 1) [20pts] List all the elements of the power set P ( { 1 , 2 , 3 } ): 2) [20pts] Find a compound proposition in disjunctive normal form equivalent to ( p q ) r . 3) [30pt] Express the negation of each of these, so that all negation symbols appear just before predicates (eg simplify these): a) x y ( P ( x, y ) Q ( x, y )) b) x y zT ( x, y, z ) 4) [30pt] Choose ONE proof. Use sentences (rather than Venn diagrams, etc). a) Prove that 3 is irrational, using a proof by contradiction (very similar to the one done in class for 2). b) Prove for every integer n , that n 2 n . You may want to handle the cases of n > 0 and n < 0 separately, and may even need to include other case(s), such as n = 0 and n = 1, etc. You can use any basic algebra to do this; I am mainly interested in your organization of the proof. c) [This is related to Ch 2.2, but you don’t have to choose it!] Prove that A ( B C ) ( A B ) ( A C ).
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