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How to Calculate Number of Relations

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 and the total number of relations is 2pq.

Let A = {a, b} and B = {c, d}. Find the number of relations from A to B.

A × B = {(a, c), (a, d), (b, c), (b, d)}.
n(A × B) = 4, the number of subsets of A × B is 24. Therefore, the number of relations from A to B will be 24.

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