   Chapter 8.2, Problem 39ES ### 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 transitive, is R ∩ S transitive? Why?

To determine

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

Explanation

Given information:

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

Proof:

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

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

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

By the definition of transitive and using that R is transitive with (a,b)R and (b,c)

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