   Chapter 8.2, Problem 36ES ### 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 34-36, assume that R is a relation on a et A. Prove or disprove each statement. If R is transitive, then R − 1 is transitive.

To determine

To prove that if R is transitive, then R1 is transitive.

Explanation

Given information:

Assume that R is a relation on a set A and R is transitive.

Proof:

Let us assume that R is transitive and let (a,b)R1 and let (b,c)R1.

By the definition of the inverse relation:

(a,b)R1(b,a)R(b,c)R1(c,b)R

By the definition of transitive (since R is transitive):

(b,a)Rand(c

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