Question

Verify that for two set A and B, n(AxB)=pq, where n(A)=p and n(B)=q . Total number of relations from A to B is 2pq

Answer 1

Answer:

Given A and B are two sets with number of elements p and q respectively.

The cartesian product of A and B=A×B={(a,b):(a∈A) and (b∈B)}

Number of elements in A×B=∣A×B∣=∣A∣.∣B∣=pq

Any relation from A to B is a subset of A×B.

Hence number of relations from A to B is the number of subsets of A×B

=2

∣A×B∣

=2

pq