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

Q: Expert Answer

To determine (a) A ⊆ B Explanation Given information: Consider the following sets. A = { x ∈ Z | for some integer a , x = 5 a + 2 } B = { y ∈ Z | for some integer b , y = 10 b − 3 } C = { z ∈ Z | for some integer c , z = 10 c + 7 } Concept used: A ⊆ B means every element of A is in elements of B. Calculation: The objective is to prove or disprove that A ⊆ B . Assume that A ⊆ B is true, then every element in the set A is an element in the set B . Assume that x ∈ A , then there is an integer a such that x = 5 a + 2 . Also, x is an element in B . There is an integer b such that x = 10 b − 3 To determine (b) Prove or disprove B ⊆ A . To determine (b) Prove or disprove B = C

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Answer 1

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Answer 2

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Discrete Mathematics With Applicat...

5th Edition

EPP + 1 other

Publisher: Cengage Learning,

ISBN: 9781337694193

Solutions

Chapter

Section

Answer 3

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Chapter

Section

Answer 4

Chapter

Section

Answer 5

To determine

(a)

A⊆B

Explanation of Solution

Given information:

Consider the following sets.

A={x∈Z|for some integer a, x=5a+2}B={y∈Z|for some integer b,y=10b−3}C={z∈Z|for some integer c, z=10c+7}

Concept used:

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

Calculation:

The objective is to prove or disprove that A⊆B.

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

Assume that x∈A, 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=10b−3

Answer 6

To determine

(b)

Prove or disprove B⊆A.

Answer 7

To determine

(b)

Prove or disprove B=C

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...

Solutions

Discrete Mathematics With Applicat...

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

Explanation of Solution

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