b. Let H be a subgroup of a group G and write a = b (mod H) if b¹a € H. Prove that this is an equivalence relation on G. Now let G = S₁ be the symmetric group on 4 letters and let H = (o) be the cyclic subgroup generated by the permutation σ = (1234). J. How many different equivalence classes are there for the relation in part a? J Is H a normal subgroup of G? Justify your answer.