Question

Let A, B, C, D, E ⊆ Z be defined as follows:
A  {2n|n ∈ Z}—that is, A is the set of all (integer)
multiples of 2;
B  {3n|n ∈ Z}; C  {4n|n ∈ Z};
D  {6n|n ∈ Z}; and E  {8n|n ∈ Z}.
a) Which of the following statements are true and which
are false?
i) E ⊆ C ⊆ A ii) A ⊆ C ⊆ E
iii) B ⊆ D iv) D ⊆ B
v) D ⊆ A vi) D ⊆ A

Determine each of the following sets.
i) C ∩ E ii) B ∪ D iii) A ∩ B
iv) B ∩ D v) A vi) A ∩ E

Answer 1

wait a sec
im working on the answer

Answer 2

If you can show the steps that would be great

Answer 3

the inputs incomplete

Answer 4

what math is that

Answer 5

I cannot write the answer because your input is incomplete

Answer 6

discrete math

Answer 7

Let A, B, C, D, E ⊆ Z be defined as follows:
A {2n|n ∈ Z}—that is, A is the set of all (integer)
multiples of 2;
B {3n|n ∈ Z}; C {4n|n ∈ Z};
D {6n|n ∈ Z}; and E {8n|n ∈ Z}.
a) Which of the following statements are true and which
are false?
i) E ⊆ C ⊆ A ii) A ⊆ C ⊆ E
iii) B ⊆ D iv) D ⊆ B
v) D ⊆ A vi) D ⊆ A

b) Determine each of the following sets.
i) C ∩ E ii) B ∪ D iii) A ∩ B
iv) B ∩ D v) A vi) A ∩ E

Answer 8

there is the problem

Answer 9

For question a;

The Set A is the set of all even integers.
The set B is the set of all multiples of 3
The set C is the set of all multiples of 4
The set D, all multiples of 6
the Set E, all multiples of 8.
True/False
i Since all multiples of 8 are multiples of 4 and all multiples of 4 are multiples of 2, this is true.
ii This is false since not all multiples of 2 are multiples of 4.
iii This is false since not all multiples of 3 are multiples of 6.
iv This is true since all multiples of 6 are multiples of 3.
v this is true since all multiples of 6 are multiples of 2.

Determine each of the following:
i. C ∩ E is the set of all numbers divisible by 4 and 8, or just E
ii. B ∪ D is the set of all numbers divisible by 3 or 6, or just B
iii. A ∩ B is the set of all numbers divisible by 2 and 3, in other words the set of all numbers divisible by 6, or D
iv. B ∩ D is the set of all numbers divisible by 3 and 6, or just D
v.) A is just the set of even numbers.
vi.) A ∩ E is the set of all numbers divisible by 2 and 8 or just E