Question

if R is a relation from a finite set A having m elements to a finite set B hving n elements, then the number of reltions from A to B is a) 2^mn b) 2^mn-1 c) 2mn d) m^n​

Answer 1

Answer=Number of relations on A = 2^{n^2}

Step-by-step explanation:

If there are n elements in set A then the total number of ordered pairs in the set A × A = n²

In other words A × A will have n² elements.

We also know that if a set has N elements then the number of subsets of A are 2^n

Therefore, for A × A there can as many relations as the number of subsets of A × A

The number of subsets of A × A = 2n^2

Therefore the number of relations = 2n^2