   Chapter 9.5, Problem 27ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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# Let A be a set with eight elements. How many relations are there on A? How many relations on A are refilexive? How many relations on A are symmetric? How many relations on A are both refilexive and symmertric?

To determine

(a)

To find how many relatinos are there on A.

Explanation

Given information:

A be a set with eight elements.

Concept used:

A relation A is a subset of A×A.

Calculation:

The objective is to determine the number or relations on set A.

A relation A is a subset of A×A.

As A×A has n2 elements, there are 2n2 subsets.

Thus, there are 2n2 relations on a set with n elements

To determine

(b)

To find how many relations on A are reflexive.

To determine

(c)

To find how many relations on A are symmetric.

To determine

(d)

To find how many relations on A are both reflexive and symmetric.

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