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Past Exam for MATH 108 - Intro Formal Mathematics at Cal State-Sacramento (CSUS)

Exam Information

Material Type:Exam 3
Professor:Staff
Class:MATH 108 - Intro Formal Mathematics
Subject:Mathematics
University:California State University - Sacramento
Term:Fall 2009
Keywords:
  • Equivalence Relation
  • Collaboration
  • Composition
  • Mathematics
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Exam 3 Math 108, Section 1 Due: Monday, December 7, 2009 at 11am This exam is an individual assignment. You are permitted to ask questions of your instructor only; collaboration of any other kind is not allowed and will be considered an act of academic dishonesty and prosecuted to the fullest extent. Your signature in the blank next to \name" below indicates that you agree to abide by the principles of academic honesty on this exam. Submit this signed cover page with your exam. There are 100 points possible. Name: 1. (10 points) Suppose R and S are relations on A=f1,2,3g. Construct relations R and S so that R-S 6= S -R. (Thus, proving relation composition is not commutative.) 2. (a) (5 points) Write a useful denial of the statement (x;y) 2 AB. (b) (10 points) Prove (AB)(AC) = A(B C) 3. (10 points) Prove (AB)(C D) (AC)(B D) 4. (10 points) Let A and B be nonempty sets. (a) Prove AB = B A if and only if A = B. (b) Is the statement in part (a) true if one of A or B is empty? Give re...
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