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Discrete Mathematics | Algebra of Sets MCQs

Discrete Mathematics | Algebra of Sets MCQs: This section contains multiple-choice questions and answers on Algebra of Sets in Discrete Mathematics.
Submitted by Anushree Goswami, on July 10, 2022

1. What is/are Idempotent Law(s)?

1. A ∪ A = A
2. A ∩ A = A
3. Both A and B
4. None of the above

Answer: C) Both A and B

Explanation:

Both A ∪ A = A and A ∩ A = A are Idempotent Laws.

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2. What is associative law?

1. (A ∪ C) = A ∪ (B ∪ C)
2. (A ∪ B) = A ∪ (B ∪ C)
3. (A ∪ C) ∪ C = A ∪ (B ∪ C)
4. (A ∪ B) ∪ C = A ∪ (B ∪ C)

Answer: D) (A ∪ B) ∪ C = A ∪ (B ∪ C)

Explanation:

Associative law means (A ∪ B) ∪ C = A ∪ (B ∪ C).

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3. What is/are commutative law(s)?

1. A ∪ B = B ∪ A
2. A ∩ B = B ∩ A
3. Both A and B
4. None of the above

Answer: C) Both A and B

Explanation:

Commutative laws are -

1. A ∪ B = B ∪ A
2. A ∩ B = B ∩ A

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4. What is distributive law?

1. A ∪ (B ∪ C) = (A ∪ B) ∩ (A ∪ C)
2. A ∩ (B ∪ C) = (A ∪ B) ∩ (A ∪ C)
3. A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)
4. A ∩ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)

Answer: C) A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)

Explanation:

Distributive law means A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C).

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5. What is Demorgan law?

1. (A ∪ B)^c=A^c ∪ B^c
2. (A ∪ B)^c=A^c ∩ B^c
3. (A ∩ B)^c=A^c ∩ B^c
4. (A ∪ B)=A^c ∩ B^c

Answer: B) (A ∪ B)^c=A^c ∩ B^c

Explanation:

Demorgan law states that (A ∪ B)^c=A^c ∩ B^c.

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6. What is/are identity law(s)?

1. A ∪ ∅ = A
2. A ∪ U = U
3. A ∩ ∅ = ∅
4. All of the above

Answer: D) All of the above

Explanation:

Identity laws are -

1. A ∪ ∅ = A
2. A ∪ U = U
3. A ∩ ∅ = ∅

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7. What is complement law?

1. A ∪ A^c= U
2. A ∩ A^c= U
3. A ∪ A= U
4. A ∩ A= U

Answer: A) A ∪ A^c= U

Explanation:

Complement law means A ∪ A^c= U.

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8. Which of the following is/are a/the complement law(s)?

1. A ∩ A^c= ∅
2. U^c= ∅
3. ∅^c = U
4. All of the above

Answer: D) All of the above

Explanation:

The following are the complement laws -

1. A ∩ A^c= ∅
2. U^c= ∅
3. ∅^c = U

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9. What is Involution law?

1. (A^c) = A
2. (A)^c = A
3. (A^c)^c = A
4. (A^c)^c)c) = A

Answer: C) (A^c)^c)c) = A

Explanation:

Involution law is (A^c)^c)c) = A.

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10. If you replace ∪, ∩, U, and ∅ in E with ∩, ∪, ∅, and U respectively, you get the dual __ of E?

1. E(U)
2. E*
3. E(∅)
4. E(∪)

Answer: B) E*

Explanation:

If you replace ∪, ∩, U, and ∅ in E with ∩, ∪, ∅, and U respectively, you get the dual E* of E.

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11. It follows that if equation E is an identity, then its dual equation E∗ ____?

1. Is not an identity
2. Is also an identity
3. Is also a dual identity
4. None of the above

Answer: B) Is also an identity

Explanation:

It follows that if equation E is an identity, then its dual equation E∗ is also an identity.

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12. Two sets with the same members are the ____ according to the Principle of Extension?

1. Similar
2. Different
3. Unique
4. Same

Answer: D) Same

Explanation:

Two sets with the same members are the same according to the Principle of Extension.

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13. What is Equal Set?

1. A=B
2. A*B
3. A+B
4. A-B

Answer: A) A=B

Explanation:

Explanation:A=B is a Equal Set.

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14. Cartesian Products are sets of all ordered pairs whose first members belong to one set and the second members to the other, denoted by the symbols ____?

1. A x B
2. A + B
3. A - B
4. A / B

Answer: A) A x B

Explanation:

Cartesian Products are sets of all ordered pairs whose first members belong to one set and the second members to the other, denoted by the symbols P x Q.

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