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Let R be the relation on Z defined by: For any a, b ∈ Z ,...

Let R be the relation on Z defined by:
For any a, b ∈ Z , aRb if and only if 4 | (a + 3b). (a) Prove that R is an equivalence relation.

(b) Prove that for all integers a and b, aRb if and only if a ≡ b (mod 4)

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