Discrete Mathematics - Chapter 6: Set Theory Question and answers rated A+ 2026

Discrete Mathematics - Chapter 6: Set
Theory Question and answers rated
A+ 2026
a set A to be a ....... of a set B as a formal universal conditional statement:

A ⊆ B ⇔ ∀x,if x ∈ A then x ∈ B. - correct answer ✔subset



....... ⊆ ...... ⇔ ∀x,if x ∈ A then x ∈ B. - correct answer ✔A, B



A ⊆ B ⇔ ∀x,if x ∈ ..... then x ∈ ........ - correct answer ✔A, B



A is a ........ of B ⇔

(1) A ⊆ B

(2) there is at least one element in B that is not in A. - correct answer ✔proper subset



Which one is correct?

1. A ⊄ B ⇔ ∃x such that x ∈ A and x ⊄ B.

2. A ⊄ B ⇔ ∃x such that x ∈ B and x ⊄ A.

3. B ⊄ A ⇔ ∃x such that x ∈ A and x ⊄ B.

4. B ⊄ A ⇔ ∃x such that x ∈ B and x ⊄ A. - correct answer ✔1, 4



Let A = {1} and B = {1, {1}}.

1. Is A ⊆ B?

2. If so, is A a proper subset of B? - correct answer ✔yes, yes

, Element Argument: The Basic Method for Proving That One Set Is a Subset of Another:

Let sets X and Y be given. To prove that X ⊆Y:

1. suppose that ..... is a particular but arbitrarily chosen element of X,

2. show that x is an element of ........ - correct answer ✔x, Y



..... = ..... ⇔ A ⊆ B and B ⊆ A. - correct answer ✔A, B



Which one is equal to A = B?

1. A ⊄ B and B ⊆ A.

2. A ⊆ B and B ⊆ A.

3. A ⊆ B and B ⊄ A. - correct answer ✔2



True or False?

if :

1. A = {m ∈ Z | m = 2a for some integer a}

2. B = {n ∈ Z | n = 2b − 2 for some integer b}

Then:

A = B - correct answer ✔true



The ...... of A and B, denoted A ∪ B, is the set of all elements that are in at least one of A or B. - correct
answer ✔union



The ....... of A and B, denoted A ∩ B, is the set of all elements that are common to both A and B. - correct
answer ✔intersection