   Chapter 8.2, Problem 38ES ### 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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# In 37-42, assume that R and S are relations on a set A. Prove or disprove each statement. If R and S are symmetric , is R ∩ S symmetric? Why?

To determine

To prove or disprove that if R and S are symmetric, then RS is symmetric.

Explanation

Given information:

Assume that R and S are relations on a set A and both are symmetric.

Proof:

Let us assume that R and S are symmetric and let (a,b)RS.

By the definition of the intersection, using that (a,b)RS:

(a,b)R(a,b)S

By the definition of symmetric and using that R is symmetric with (a,b)R:

(b,a)R

By the definition of symmetri

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