Let be a set with elements.

MATHEMATICS · Multi-part · CBSE · Mathematics · Relations and Functions · Relations and Functions

Problem

Let

A

be a set with

n

elements. (a) State the condition that a relation

R

A

must satisfy to be symmetric. (b) Prove that the total number of symmetric relations on

A

2^{\frac{n(n+1)}{2}}

. (c) Find the number of symmetric relations when

n=3