In each case determine if the given relation R on A is an equivalence relation. Justify your answer. (a) A = Z and aRb if ab ≥ 0. (b) A = Z and aRb if 5|a − b. (c) A = Z and aRb if 5|a^2-b^2. (d) A =...

In each case determine if the given relation R on A is an equivalence relation.
Justify your answer.
(a) A = Z and aRb if ab ≥ 0.
(b) A = Z and aRb if 5|a − b.
(c) A = Z and aRb if 5|a^2-b^2.
(d) A = Z and aRb if 5|a^3-b^3.
(e) A = Z and aRb if 5|a^4-b^4
(f) A = Z and aRb if 5|a^5-b^5
(g) A = R2 and (a, b)R(c, d) if a = c.
(h) A = R2 and (a, b)R(c, d) if a^2+b^2=c^2+d^2.