Question

If n(A) = m and n(B) = n then the total number of non-empty relations that can be defined from A to B?

• A. m${}^{\text{n}}$
• B. n${}^{\text{m}}$
• C. (2)${}^{\text{mn}}$ -1
• D. (2)${}^{\text{mn}}$

Answer 1

The correct option is C (2)${}^{\text{mn}}$ -1

Given: n(A) = m and n(B) = n
Then total number of relations from A to B = (2)${}^{\text{mn}}$
But total number of non-empty relations from A to B =(2)${}^{\text{mn}}$ - 1
(As empty set is also a subset of A x B)