Consider the relation R defined on the set Z as follows: ∀m, n ∈ Z, (m,...

Consider the relation R defined on the set Z as follows: ∀m, n ∈ Z, (m, n) ∈ R if and only if m + n = 2k for some integer k. For example, (3, 11) is in R because 3 + 11 = 14 = 2(7).

(a) Is the relation reflexive? Prove or disprove.

(b) Is the relation symmetric? Prove or disprove.

(c) Is the relation transitive? Prove or disprove.

(d) Is it an equivalence relation? Explain.

Expert Solution

Colby Messinger answered 9 months ago

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