This preview shows page 1. Sign up to view the full content.
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.] ...
View
Full
Document
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.
 Spring '08
 EVINSON
 Calculus, Logic

Click to edit the document details