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​

Answer 1

Answer:

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

n(A×B)=n(A).n(B)=mn

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

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

thank you!!

Answer 2

Answer:

2^mn - 1

Step-by-step explanation:

The total no. of elements in AxB=n(A)xn(B)=mn

The total no. of subsets = Total no. of relations

The total n. of subsets =2^no. of sets

Total no. of relations=2^mn

This set also contains one empty set

therefore the no. of non-empty sets=2^mn - 1

Hope it helps!