   Chapter 8.2, Problem 40ES ### 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 set A. Prove or disprove each statement. If R and S are reflexive, is R ∪ S reflexive? Why?

To determine

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

Explanation

Given information:

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

Proof:

Let us assume that R and S are reflexive and let aA.

By the definition of reflexive and using that R is reflexive:

(a,a)R

By the definition of reflexive and using that S is reflexive:

(a,a)S

By the definition of the union, using that (a,a

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