Question

Let A be a finite set containing n distinct elements. The number of relations that can be defined on A is:

• A. $2^n$
• B. $n^2$
• C. $2^{n^2}$
• D. 2n

Answer 1

Answer: (C)

$2^{n^2}$

Since $A$ contains $n$ distinct elements, therefore, $A\times A$ contains $n\times n=n^2$ distinct elements. since every subset of $A\times A$ is a relation on $A$., therefore, number of relations on $A$ is equal to the order of the power set of $A\times A$, is equal to the order of the power set of $A\times A$, i.e., $2^{n^2}$