homework1

homework1 - R ( P R ) ( Q R ). b) Verify that P ( Q R ) ( P...

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HOMEWORK 1. DUE FRIDAY, 4/1. SERIOUSLY. MATH 131A, SPRING 2011, STOVALL To turn in: Problem 1: Let P and Q be mathematical statements. Use truth tables to verify that a) ( P Q ) ( P ) ( Q ) b) ( P Q ) ( P ) ( Q ) c) ( P = Q ) P ( Q ) Problem 2: Simply the following negations: a) [( P = Q ) = ( S = U )] b) [ P 1 and for every n N , P n = P n +1 ] c) [For every natural number n , there exists a natural number m such that P ( n,m )] (Here P ( n,m ) is a statement that depends on n and m , e.g. “ n is prime and m n ”.) Problem 3: Let A,B , and C be sets. Show that A \ ( B C ) = ( A \ B ) ( A \ C ). Recommended: Let P,Q,R be mathematical statements. a) Verify that ( P Q )
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Unformatted text preview: R ( P R ) ( Q R ). b) Verify that P ( Q R ) ( P Q ) ( P R ). c) Give three specic, concrete mathematical statements P,Q,R such that P ( Q R ) is true but ( P Q ) R is false. Simplify the following negations: a) [ n N , P n Q n ] b) [For some n N , P ( n,m ) holds for every m N ] Let A,B,C be sets. Prove that a) A ( B \ C ) = ( A B ) \ ( A C ) . b) ( A \ B ) B = A if and only if B A . 1...
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