   Chapter 8.2, Problem 42ES ### 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 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.

Calculation:

Given statement: Let R and S are relations on the set A. If R an S are transitive, then RS is transitive

The given statement is false, which we will justify with a counterexample.

Let R={(0,1)} and S={(1,2)} with A={0,1,2}.

By the definition of the union:

RS={(0,1),(1,2)}

R is transitive, because the if-statement “ (a,b

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