   Chapter 8.1, Problem 1ES ### 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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# As in Example 8.1.2, the congruence modulo 2 relation E is defined from Z to Z as follows: For every ordered ( m , n ) ∈ Z × Z . m E n   ⇔     m − n   is       even . Is 0 E 0? Is 5 E 2? Is (6,6) ∈ E ? Prove that for any even integer n , n E 0 .

To determine

(a)

Whether 0 E 0, 5 E 2, 6, 6) ∈ E and (-1, 7) ∈ E are true or not for the relation E.

Explanation

Given information:

For every ordered pair (m,n)Z×Z, m E n ⇔ m - n is even.

Calculation:

m E nmn is even for every ordered pair (m,n)Z×Z.

0E0 is true because 0 − 0 = 0 is even (since 0 is divisible by 2) and (0,0)Z×Z.

5E2 because 5 − 2 = 3 is not even (since 3 is not divisible by 2) for every (5,2)Z×Z

To determine

(b)

Prove that for any even integer n, n E 0.

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