   Chapter 8.3, Problem 2ES ### 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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# Each of the following partitions of { 0 ,   1 ,   2 ,   3 ,   4 } induces a relation R on { 0 ,   1 ,   2 ,   3 ,   4 } . In each case, find the ordered pairs in R. a. { 0 ,   2 } ,   { 1 } ,   { 3 ,   4 } b. { 0 } ,   { 1 ,   3 ,   4 } ,   { 2 } c. { 0 } ,   { 1 ,   2 ,   3 ,   4 }

To determine

(a)

To find the ordered pairs in R for the partition {0,2},{1},{3,4}.

Explanation

Given information:

The following partitions of {0, 1, 2, 3, 4} induces a relation R on {0, 1, 2, 3, 4}.

{0,2},{1},{3,4}

Calculation:

Given partitions are {0,2},{1},{3,4}.

We know that if R is the induced relation on {0,1,2,3,4} by the partition then xRyx and y lies in the same subset of the partition.

We have,

0R0, 0R2, 2R2, 2R0  {0,2}1R1       �

To determine

(b)

To find the ordered pairs in R for the partition {0},{1,3,4},{2}.

To determine

(c)

To find the ordered pairs in R for the partition {0},{1,2,3,4}.

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