homework8 - LOGIC AND PROOF HOMEWORK 8 1. Consider the...

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Unformatted text preview: LOGIC AND PROOF HOMEWORK 8 1. Consider the function f: {1,2,3,4,5,6,7} {0,1,2,3,4,5,6,7,8,9} given as f{(1,3), (2,8), (3,3), (4,1), (5,2), (6,4), (7,6)} Find f({1,2,3}) and f‐1({0,5,9}). 2. Let g: x by g(m,n) = 2m3n, let A = {1,2,3}, and let C = {1,4,6,9,12,16,18}. Find g(A x A) and g‐1(C). 3. Prove that the converse of Theorem 4.5.1 (a) is true when f is 1‐1. 4. Provide a counterexample to show that the converse of Theorem 4.5.1 (a) is not true when f is not 1‐1. 5. Use an epsilon argument to prove that if xn L and yn M, then xn – yn L – M. 6. Use an epsilon argument to prove that xn = converges. 7. Use = 1/3 to show that xn = diverges. 8. 4.6.9 (part e) [Hint: Prove that the sequence is increasing and (by induction) that it is bounded above by 4. It therefore must converge (see Calculus, Section 12.1) Determine the limit.] ...
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This note was uploaded on 09/22/2011 for the course MAC 2311 taught by Professor Evinson during the Spring '08 term at University of Central Florida.

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