Let R be a relation from N to N defined by R = {(a, b): a, b ∈ N and a = b2}. Are the following true?     (3 marks)

(i) (a, a) ∈ R, for all a ∈ N

(ii) (a, b) ∈ R, implies (b, a) ∈ R

(iii) (a, b) ∈ R, (b, c) ∈ R implies (a, c) ∈ R.

Justify your answer in each case.