Question:
If R is a relation from a finite set A having m elements of a finite set B having n elements, then the number of relations from A to B is
(a) 2mn
(b) 2mn − 1
(c) 2mn
(d) mn
Solution:
(a) 2mn
Given: n(A) = m
n(B) = n
$\therefore n(A \times B)=m n$
Then, the number of relations from $A$ to $B$ is $2^{m n}$.