Presentation on theme: "Membership Tables: Proving Set Identities with One Example"— Presentation transcript:
1 Membership Tables: Proving Set Identities with One Example
2 Proof techniques we teach in Discrete Mathematics Direct ProofsProofs by ContradictionProofs by ContrapositiveProofs by CasesMathematical Induction (Strong Form?)Proof techniques we do NOT teach in Discrete MathematicsProof by one exampleProof by two examplesProof by a few examplesProof by many examples
3 Two sets X and Y are equal if X and Y have the same elements. To prove sets X and Y are equal, prove ifthen , and if , then
4 Example: Determine the truth value of Proof: Let Then x is a member of X, or x is a member of . Hence, x is a member of X, or x is a member of Y and x is a member of Z. If x is a member of X, then x is a member of and x is a member of .Otherwise, x is a member of Y and Z and hence a member of and Either way, x is a member of and Therefore,.Now show the other direction.
9 “Never underestimate the value of a good example.” --Tom Hern, Bowling Green State UniversityInvited Address at 2005 Fall Meeting of theOhio Section of MAADiscrete Mathematics textbooks containing descriptions of membership tables:1) Kenneth H. Rosen, Discrete Mathematics and Its Applications, 5th Ed., McGraw Hill, 2003, p. 91.2) Ralph P. Grimaldi, Discrete and Combinatorial Mathematics, 5th Ed., Pearson, 2004, pp