Let - be a relation on a set X defined as below. Determine whether is an equivalence relation on X and if it is, find the equivalence classes and the quotient set. a) X = Z, x ~ y + x +y is even. b) X = Z, x ~y A x +y is odd. c) X = Z, x ~ y + x+y is divisible by 3.

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A: Introduction :

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