Homework 6 - MATH 74 HOMEWORK 6 (DUE WEDNESDAY OCTOBER 17)...

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MATH 74 HOMEWORK 6 (DUE WEDNESDAY OCTOBER 17) Assume a calculus-level familiarity with arithmetic in this problem set. 1. Let A = { a 2 - b 2 : a,b Z } and B = { 2 k - 1 : k Z } . 1(a). Is A B ? If yes, prove it. If no, explain why. (This means: give a counterexample, and as much discussion that a casual reader might need to be convinced that it is a counterexample.) 1(b). Is B A ? If yes, prove it. If no, explain why. 1(c). Is A = B ? If yes, explain why. If no, explain why. 2. Let A , B , and C be sets. 2(a). Suppose that A B . Is it necessarily also true that then A B B C ? If so, prove it. If not, explain why. 2(b). Suppose that A C B C . Is it necessarily also true that A B ? If so, prove it. If not, explain why. 3. Let A , B , and C be sets. Suppose that A B and B C are nonempty. Is it necessarily also true that A C is nonempty? If so, prove it. If not, explain why. 4.
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This note was uploaded on 02/10/2010 for the course MATH 74 taught by Professor Courtney during the Fall '07 term at University of California, Berkeley.

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