   # Let A = { x ∈ Z | x = 6 a + 4 for some integer a } , B = { y ∈ Z | y = 18 b − 2 for some integer b } , and C = { z ∈ Z | z = 18 c + 16 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 7ES
Textbook Problem
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## Let   A = { x ∈ Z | x = 6 a + 4   for   some integer  a } , B = { y ∈ Z | y = 18 b − 2   for   some integer  b } ,   and C =   { z ∈ Z | z = 18 c + 16   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 sets.

A={xZ|x=6a+4 for some integer a}B={yZ|y=18b2 for some integer b}C={zZ|z=18c+16 for some integer c}

Concept used:

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

Calculation:

The objective is to prove or disprove the statement.

AB

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

Let xA, then there is an integer a such that x=6a+4 and x is an element in B.

Thus, there is an integer b such that x=18b2.

Since, x=6a+4 and x=18b2, then

6a+4=18b2

To determine

(b)

Prove or disprove BA

To determine

(c)

Prove or disprove B=C

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