Question

Let S = {A, B, C, D, E, F, G, H, I, J} be the set consisting of the following elements:

A = N, B = 2N , C = 2P(N) , D = [0, 1), E = ∅, F = Z × Z, G = {x ∈ N|x 2 + x < 2}, H = { 2 n 3 k |n, k ∈ N}, I = R \ Q, J = R.

Consider the relation ∼ on S given by: U ∼ W if there exists an injective function f : U → W and an injective function g : W → U. Give a brief reason why ∼ is an equivalence relation, and write down the equivalence classes of this relation (you should give brief justifications for your answers).1

Answer 1