Question

two finite sets A and B have p and q elements . the total number of subset of A and B is 144.find the value of ( p+ q)? ​

Answer 1

Step-by-step explanation:

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∣=2pq