(a) Let A = {(1,3),(2,4),(-4,-8),(3,9),(1,5),(3,6)}. Define a relation R on A as follows: (a,b)R(c,d) if ad=bc. List the equivalence classes of R.

(b) Let a,b ∋ Z

(i) Define aRb and only if a^3 ≡ b^3 (mod 7).

Prove that R is an equivalence relation on Z.

(ii) Define a ≅ b if and only if a ≡ b (mod 7), What are the equivalence classes for ≅?

Please also explain your answers/working out as you go along (if possible). thanks