The total number of relations that can be defined from a set A to a set B is the number of possible subsets of A × B. If n(A)=p and n(B)=q, then n(A × B)= p q. So, the total number of relations is 2^pq.

Now,

A × A = {(a, a), (a, b), (b, a), (b, b)}

Total number of relations are all possible subsets of A × A:

{ Φ, {(a, a)}, {(a, b)}, {(b, a)}, {(b, b)}, {(a, a), (a, b)}, {(a, a), (b, a)}, {(a, a), (b, b)}, {(a, b), (b, a)}, {(a, b), (b, b)}, {(b, a), (b, b)}, {(a, a), (a, b), (b, a)}, {(a, b), (b, a), (b, b)}, {(a, a), (b, a), (b, b)}, {(a, a), (a, b), (b, b)}, {(a, a), (a, b), (b, a), (b, b)}}

n(A) = 2 ⇒ n(A × A) = 2 × 2 = 4

∴ Total number of relations = 2⁴ = 16