   # Let A = { n ∈ Z | n = 5 r for some integer r } and B = { m ∈ Z | m = 20 s for some integer s } . Prove or disprove each of the following statements. a. A ⊆ B b. B ⊆ A ### 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 4ES
Textbook Problem
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## Let A = { n ∈ Z | n = 5 r   for   some integer  r } and B = { m ∈ Z | m = 20 s for some integer  s } . Prove or disprove each of the following statements.a. A ⊆ B b. B ⊆ A

To determine

(a)

Is AB ? Explain.

### Explanation of Solution

Given information:

Two sets A and B are defined as follows.

A={n|n=5r for some integer r} ,

B={m|m=20s for some integer s}

Concept used:

To prove AB, need to prove for enery xA,xB, to prove AB, need to prove there exists an xA, such that xB.

Calculation:

Let X be an element of A. Then there exists an integer r such that x=5r

To determine

(b)

Is BA ? False.

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