Relations 188 give either a proof 15. Suppose Ri and R2 are relations on A. For
ID: 2976847 • Letter: R
Question
Relations 188 give either a proof 15. Suppose Ri and R2 are relations on A. For each part, or a counterexample to justify your answer. be reflexive? (a) If R1 and R2 are reflexive, must R1 R2 (b) If Ri and R2 are symmetric, must RI R2 be symmetric? (c) If Ri and R2 are transitive, must R1 R2 be transitive? 16. Suppose R and s are reflexive relations on A. Prove that R o Sis reflexive 17. Suppose and S are symmetric relations on A Prove that R o S is sym- R 18. Suppose R and S are transitive relations on A. Prove that if S o RSR o S then R o S is transitive. 19. Consider the following putative theorem. Theorem? Suppose R is a relation on A, and define a relation S on 9 (A) as follows:Explanation / Answer
R is transitive if and only if R • R is a subset of R. R is reflexive if and only if D(A) is a subset of R. R is symmetric if R-1 is a subset of R. R is antisymmetric if and only if the intersection of R and R-1 is D(A). R is asymmetric if...