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

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Advance Math

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. Forexample, (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.

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