# The number of relations on a finite set having 5 elements is

Question:

The number of relations on a finite set having 5 elements is

Solution:

Let R be a relation on A, where A contains 5 elements.

R is a subset of A × A.

Number of elements in A × A = 5 × 5 = 25

Number of relations $=$ Number of subsets of $A \times A=2^{25}$

Hence, the number of relations on a finite set having 5 elements is $2^{25}$.