Question

Given two finite sets A and B such that n(A) = 3, n(B) = 3. Then total number of relations from A to B is _____.

• A. 8
• B. 6
• C. 4
• D. 512

Answer 1

The correct option is D

512

Here n(A × B) = 3 × 3 = 9

Since every subset of A × B defines a relation from A to B, the number of relations from A to B is equal to the number of subsets of A $\times$ B = $2^{\text{n(A}\times \text{B)}}$
= $2^9$
= 512