Question -
Answer -
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) = pq.
So, the total number of relations is 2pq.
Now,
A × A = {(a, a), (a, b), (b, a), (b, b)}
Total number of relations are all possible subsets of A × A:
[{(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