   # Let C = { n ∈ Z | n = 6 r − 5 for some integer r } and D = { m ∈ Z | m = 3 s + 1 for some int eger s } Prove or disprove each of the following statements. a. C ⊆ D b. D ⊆ C ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
Publisher: Cengage Learning,
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
Publisher: Cengage Learning,
ISBN: 9781337694193
Chapter 6.1, Problem 5ES
Textbook Problem
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## Let C = { n ∈ Z | n = 6 r − 5 for some integer r } and D = { m ∈ Z | m = 3 s + 1   for   some     int eger   s } Prove or disprove each of the following statements.a. C ⊆ D b. D ⊆ C

To determine

(a)

CD

### Explanation of Solution

Given information:

C={n|n=6r5 for some integer r} And D={m|m=3s+1 for some integer s}.

Concept used:

The objective is to prove or disprove CD.

Need to show that every element of C is in D.

Calculation:

Suppose nC, then n=6r5 for some integer r.

Let s=2r2

To determine

(b)

Prove or diprove DC.

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