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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.

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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).

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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.

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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.

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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

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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)

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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

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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

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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.

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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.

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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)'

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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

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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.

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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.

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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.

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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.

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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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