   Chapter 8.1, Problem 21ES ### 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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# Define relation R and S on R as follows: R = { ( x , y ) ∈ R × R|x<y } and S= { ( x , y ) ∈ R × R|x=y } , That is, R is the “less than” relation and S is the “equals” relation on R. Graph R , S , R ∪ S , and R ∩ S in the in the Cartesian plane.

To determine

To graph R, S, RS, and R nS in the Cartesianplane.

Explanation

Given information:

Define relations R and S on R as follows:

R = {(x, y)R xR | x < y} and

S = {(x, y)R xR | x = y}.

That is, R is the “less than” relation and S is the “equals” relation on R. Graph R, S, RS, and R nS in the Cartesianplane.

Calculation:

R = {(x, y)R xR | x < y}

S = {(x, y)R xR | x = y}

Graph R

R contains all ordered pairs (x, y) for which x

Graph S:

S contains all ordered pairs (x, y) for which x = y, which is the straight line y = x.

Graph union:

The graph of the union RS contains all ordered pairs that belong to the region of R or belong to the region of S. thus the graph of the union then contains the straight line y = x in the graph of S and the region where x

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