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 relation

R

A

is called reflexive and symmetric if it is both reflexive and symmetric. (a) Show that every such relation must contain exactly

n

ordered pairs of the form

(a,a)

with

a\in A

. (b) Obtain a general formula for the total number of relations on

A

that are simultaneously reflexive and symmetric. (c) Using your formula, determine the number of reflexive and symmetric relations on a set with

5

elements.