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 $2^{25}$.