Question

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

Answer 1

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 × A = 2²⁵

Hence, the number of relations on a finite set having 5 elements is 2²⁵.