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Unformatted text preview: Math 199, Fall 2009. Homework Set 1 1 Homework Set 1 Rules: Please list your collaborators for each problem. You better bring it as otherwise the grader will smite you. Finally, reminder that this assignment is meant to entertain you and please dont be afraid to think! 1 Problem 1. In this problem, let X be the universal set with subsets A ; B ; C of X . Prove the following (in)equalities. (a) A [ ( B [ C ) = ( A [ B ) [ C : (b) A \ ( B \ C ) = ( A \ B ) \ C : (c) A [ ( B \ C ) = ( A [ B ) \ ( A [ C ) : (d) ( A \ B ) c = A c [ B c : (e) ( A n B ) \ ( C n B ) = ( A \ C ) n B : (f) B n A A c : (g) A n B A \ B : Problem 2. Prove that if A B and C D , then A B C D . Problem 3. Let A X and B ; C Y . Prove that A ( B \ C ) = ( A B ) \ ( A C ) : Problem 4. Let a ; b ; c 2 Z . We say a j b if there exists an integer q in Z such that qa = b . Prove the following: (a) If a j b and b j a , then a = b ....
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