   Chapter 8.1, Problem 23ES ### 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
1 views

# Define relations R and S on R as follows: R = { ( x , y ) ∈ R × Ry=|x| }       and S= { ( x , y ) ∈ R × R|y=1 } . Graph R , S , R ∪ S , and R ∩ S , and in the Cartesian plane.

To determine

GraphR, S, RS, and R nS in the Cartesian plane.

Explanation

Given information:

Define relations R and S on R as follows:

R = {(x,y)∈R xR | y = |x|} and

S = {(x, y)R xR | y = 1}.

Calculation:

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

S = {(x, y)R xR | y = 1} Graph R

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

Note that y=|x| is the (standard) absolute value function.

Graph S:

S contains all ordered pairs (x, y) for which y = 1, which is the horizontal line at y = 1.

Graph union: RS

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 both the vertical line y = 1 in the graph of S and the absolute value function y=|x| in the graph of R

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