Discrete Mathematics | Boolean Algebra MCQs

Discrete Mathematics | Boolean Algebra MCQs: This section contains multiple-choice questions and answers on Boolean Algebra in Discrete Mathematics.
Submitted by Anushree Goswami, on November 01, 2022

1. The Boolean Algebra is a complemented ____ lattice.

  1. Associative
  2. Distributive
  3. Commutative
  4. Supplementary

Answer: B) Distributive

Explanation:

The Boolean Algebra is a complemented distributive lattice.


2. Boolean Algebra is denoted by -

  1. (B, ∧,∨,',1)
  2. (B, ∧,∨,',0)
  3. (B, ∧,',0,1)
  4. (B, ∧,∨,',0,1)

Answer: D) (B, ∧,∨,',0,1)

Explanation:

Boolean Algebra is denoted by (B, ∧,∨,',0,1).


3. B is a set on which two binary operations ∧ (*) and ∨(+) and a ____ operation (complement) are defined.

  1. Unary
  2. Binary
  3. Ternary
  4. None

Answer: A) Unary

Explanation:

B is a set on which two binary operations ∧ (*) and ∨(+) and a unary operation (complement) are defined.


4. Since (B,∧,∨) represents a ____ distributive lattice, each element of B has a unique complement.

  1. Complemented
  2. Supplemented
  3. Adjacent
  4. None

Answer: A) Complemented

Explanation:

Since (B,∧,∨) represents a complemented distributive lattice, each element of B has a unique complement.


5. What is/are the property/ies of Boolean Algebra?

  1. Commutative
  2. Distributive
  3. Identity
  4. All of the above

Answer: D) All of the above

Explanation:

The properties of Boolean Algebra are -

  1. Commutative
  2. Distributive
  3. Identity

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6. Commutative Property states that -

  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 Property states that -

  1. a+b = b+a
  2. a*b=b *a

7. Distributive Property states that -

  1. a+(b*c)=(a+b)*(a+c)
  2. a*(b+c)=(a*b)+(a*c)
  3. Both A and B
  4. None of the above

Answer: C) Both A and B

Explanation:

Distributive Property states that -

  1. a+(b*c)=(a+b)*(a+c)
  2. a*(b+c)=(a*b)+(a*c)

8. Identity Property states that -

  1. a+0=a
  2. a *1=a
  3. Both A and B
  4. None of the above

Answer: C) Both A and B

Explanation:

Identity Property states that -

  1. a+0=a
  2. a *1=a

9. Complemented Laws states that -

  1. a+a'=1
  2. a * a'=0
  3. Both A and B
  4. None of the above

Answer: C) Both A and B

Explanation:

Complemented Laws states that -

  1. a+a'=1
  2. a * a'=0

10. If A itself is a Boolean Algebra, then (A,*, +,', 0,1) is a ____ of B.

  1. Sub-algebra
  2. Sub-Boolean Algebra
  3. Both A and B
  4. None of the above

Answer: C) Both A and B

Explanation:

If A itself is a Boolean Algebra, then (A,*, +,', 0,1) is a sub-algebra or sub-boolean algebra of B.


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11. Subsets of a Boolean Algebra can be ____, but may or may not be subalgebras because B may not be closed.

  1. Algebra
  2. Boolean Algebra
  3. Sub-algebra
  4. Sub-Boolean Algebra

Answer: B) Boolean Algebra

Explanation:

Subsets of a Boolean Algebra can be Boolean algebras, but may or may not be subalgebras because B may not be closed.


12. If two Boolean algebras B and B1 go together one to one, then they are called ____ and are preserved for all elements from B including a, b in B.

  1. Isomorphic
  2. Boolean Functions
  3. Boolean Expressions
  4. None of the above

Answer: A) Isomorphic

Explanation:

If two Boolean algebras B and B1 go together one to one, then they are called isomorphic and are preserved for all elements from B including a, b in B.


13. Which of the following are Isomorphic-Boolean Algebras?

  1. f (a+b)=f(a)+f(b)
  2. f (a*b)=f(a)*f(b)
  3. f(a')=f(a)'
  4. All of the above

Answer: D) All of the above

Explanation:

The following are Isomorphic-Boolean Algebras -

  1. f (a+b)=f(a)+f(b)
  2. f (a*b)=f(a)*f(b)
  3. f(a')=f(a)'

14. Which of the following is/are the basic property/ies of Boolean Algebra?

  1. Idempotent Law
  2. Commutative Property
  3. Associative Property
  4. All of the above

Answer: D) All of the above

Explanation:

The following are the properties of Boolean Algebra -

  1. Idempotent Law
  2. Commutative Property
  3. Associative Property

15. Which of the following is/are NOT the basic property/ies of Boolean Algebra?

  1. Absorption Laws
  2. Identity Laws
  3. Null Laws
  4. Evolution Laws

Answer: D) Evolution Laws

Explanation:

Evolution Laws is NOT the basic property of Boolean Algebra.


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16. Which of the following statement is TRUE?

  1. 0 ≤ a ≤ 1 ∀ a ∈ B.
  2. There is a unique complement b' for every element b.
  3. Both A and B
  4. None of the above

Answer: C) Both A and B

Explanation:

The following statements are TRUE -

  1. 0 ≤ a ≤ 1 ∀ a ∈ B.
  2. There is a unique complement b' for every element b.

17. When a Boolean Expression based on n variables specifies a function from A'' to A, it is called a Boolean ____.

  1. Algebra
  2. Expression
  3. Function
  4. Law

Answer: C) Function

Explanation:

When a Boolean Expression based on n variables specifies a function from A'' to A, it is called a Boolean Function.


18. ____ descriptions of functions are always possible.

  1. Tabular
  2. Graphical
  3. Analytical
  4. None

Answer: A) Tabular

Explanation:

Tabular descriptions of functions are always possible.


19. ____ can be used as an alternative method of expressing functions.

  1. Function
  2. Expression
  3. Law
  4. Algebra

Answer: B) Expression

Explanation:

Expressions can be used as an alternative method of expressing functions.


20. Two-valued Boolean algebra considers all functions from ____ as Boolean functions.

  1. [0, 1]2 to [0, 1]
  2. [0, 1]3 to [0, 1]
  3. [0, 1]n-1 to [0, 1]
  4. [0, 1]n to [0, 1]

Answer: D) [0, 1]n to [0, 1]

Explanation:

Two-valued Boolean algebra considers all functions from [0, 1]n to [0, 1] as Boolean functions.



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