Give an example of two equivalence relations R and S on the set A = {1, 2, 3} such that RUS is not an equivalence relation. 6. %3D
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- Let be a relation defined on the set of all integers by if and only if sum of and is odd. Decide whether or not is an equivalence relation. Justify your decision.Give an example of a relation R on a nonempty set A that is symmetric and transitive, but not reflexive.Prove Theorem 1.40: If is an equivalence relation on the nonempty set , then the distinct equivalence classes of form a partition of .