Let ∼be the relation on Z defined as follows: For every m, n ∈Z, m ∼n if, and only if, 5 | (m2 −n2 ). (a) Determine whether ∼is reflexive. Justify your answer. (b) Determine whether ∼is symmetric. Justify your answer. (c) Determine whether ∼is transitive. Justify your answer.

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