Question

Let n (A) = m, and n (B) = n. Then the total number of non-empty relations that can be defined from A to B is

(A) mⁿ 

(B) n^m – 1

(C) mⁿ – 1 

(D) 2^mn – 1

Answer 1

Answer is (D)

We have, n(A) = m and n(B) = n

n(A x B) = n(A). n(B) = mn

Total number of relation from A to B = Number of subsets of A x B = 2^mn

So, total number of non-empty relations = 2^mn – 1