# 5 Is It Possible To Have A Relation On The Set A B C That Is Both Symmetric And

(5) Is it possible to have a relation on the set {a,b,c} that is both symmetric and antisymmetric? If so, give an
example (similar to zyBooks exercise 5.2.3 (b)). (6 points)
(8) Let n ∈ Z+. We can deﬁne the relation Mn on the domain Z where x Mn y if and only if x mod n = y mod n. Answer the following questions to reach a conclusion about (Z+,D’): (4+4+4+2+6 points each for 20 points total)(8a) Prove that for every n, Mn is reﬂexive. (8b) Prove that for every n, Mn is transitive. (8c) Prove that for every n, Mn is symmetric. (8d) Conclude that Mn is an equivalence relation. (8e) Consider the equivalence relation M5. List all distinct equivalence classes for M5.
5) Actually we on non-empty we can always define relation which is both symmetric and anti-symmetirc.There, it is possible to have relation on the set {a, b, c} that is both symmetric and…

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