   Chapter 8.2, Problem 28ES ### 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 9-33, determine whether the given relation is reflexive, symmetric, transitive, or none of these. Justify your answer. Let A = R × R . A relation F is defined on A as follows: For every ( x 1 , y 1 ) and ( x 2 , y 2 ) in A, ( x 1 , y 1 ) F ( x 1 , x 2 ) ⇔ x 1 = x 2 .

To determine

To justify whether the given relation is reflexive, symmetric, transitive, or none of these.

Explanation

Given information:

Let A = R × R .

A relation F Is defined on A as follows: For all (x1,y1) and (x2,y2) in A, (x1,y1) F (x2,y2)x1=x2.

Calculation:

A= R×R

F={(( x 1, y 1),( x 2, y 2))A|x1=x2}

Reflexive:

The relation F Is reflective if ((x1,y1),(x1,y1))F for every element (x1,y1)A.

Since x1=x1, we know that ((x1,y1),(x1,y1))F for all elements (x1,y1)A.

Thus F Is reflexive

Symmetric:

The relation F on a set A is symmetric if ((x1,y1),(x2,y2))F whenever ((x2,y2),(x1,y1))F

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