R = {(a, b): a, b ∈ N and a = b^{2}}

(i) It can be seen that 2 ∈ N; however, 2 ≠ 2^{2} = 4.

Therefore, the statement “(a, a) ∈ R, for all a ∈ N” is not true.

(ii) It can be seen that (9, 3) ∈ N because 9, 3 ∈ N and 9 = 3^{2}.

Now, 3 ≠ 9^{2} = 81;

therefore, (3, 9) ∉ N Therefore, the statement “(a, b) ∈ R, implies (b, a) ∈ R” is not true.

(iii) It can be seen that (9, 3) ∈ R, (16, 4) ∈ R because 9, 3, 16, 4 ∈ N and 9 = 3^{2} and 16 = 4^{2}.

Now, 9 ≠ 4^{2} = 16; therefore, (9, 4) ∉ N Therefore, the statement “(a, b) ∈ R, (b, c) ∈ R implies (a, c) ∈ R” is not true.