   # Let A = { x ∈ z | x = 5 a + 2 for some integer a } . B = { y ∈ Z | y = 10 b − 3 for some integer b } , and C= { z ∈ Z | z = 10 c + 7 for some integer c } . Prove or disprove each of the following statements. a. A ⊆ B b. B ⊆ A c. B = 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 6ES
Textbook Problem
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## Let A = { x ∈ z | x = 5 a +   2   for   some integer  a } . B = { y ∈ Z | y = 10 b − 3     for   some   integer  b } ,   and C= { z ∈ Z | z = 10 c + 7   for   some integer  c } . Prove or disprove each of the following statements.a. A ⊆ B b. B ⊆ A c. B = C

To determine

(a)

AB

### Explanation of Solution

Given information:

Consider the following sets.

A={xZ|for some integer a, x=5a+2}B={yZ|for some integer b,y=10b3}C={zZ|for some integer c, z=10c+7}

Concept used:

AB means every element of A is in elements of B.

Calculation:

The objective is to prove or disprove that AB.

Assume that AB is true, then every element in the set A is an element in the set B.

Assume that xA, then there is an integer a such that x=5a+2.

Also, x is an element in B.

There is an integer b such that x=10b3

To determine

(b)

Prove or disprove BA.

To determine

(b)

Prove or disprove B=C

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