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 A x+y is even. %3D...

Extracted text: 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 A x+y is even. %3D b) X = Z, x ~y A x +y is odd. c) X = Z, x ~~y + x+y is divisible by 3. %3D d) X = Z, x ~ y = xy # 0. e) X = Z, x ~y A xy > 0. f) X = R × R, (x1, Yı) ~ (x2, Y2) → x1 = Y1. xỉ + yỉ = x3 + y3. + |x1 – Yı| = |x2 – Y2|. g) X = R × R, (¤1, Y1) ~ (x2, Y2) %3D h) X = R x R, (x1, Yı) ~ (x2, Y2)