   Chapter 8.1, 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
1 views

# Prove that for all integers m and n,m-n is even if, and only if, both m and n are even or both m and n are odd.

To determine

To prove:

That for all integers m and n, m - n is even if, and only if, both m and n are even or both m and n are odd.

Explanation

Proof:

Let us consider m,n where is the set of integers.

mn is even

Case I:

Suppose m is even and n is odd, then

m=2q,n=2p+1,p,qmn=2q(2p+1)=2q2p1=2(qp)1=2k1,k

Which is odd, and this is a contradiction.

Case II:

Suppose m is odd and n is even, then

m=2q+1,n=2p,p,qmn=2q+12p=2

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