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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.
- Associative
- Distributive
- Commutative
- Supplementary
Answer: B) Distributive
Explanation:
The Boolean Algebra is a complemented distributive lattice.
2. Boolean Algebra is denoted by -
- (B, ∧,∨,',1)
- (B, ∧,∨,',0)
- (B, ∧,',0,1)
- (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.
- Unary
- Binary
- Ternary
- 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.
- Complemented
- Supplemented
- Adjacent
- 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?
- Commutative
- Distributive
- Identity
- All of the above
Answer: D) All of the above
Explanation:
The properties of Boolean Algebra are -
- Commutative
- Distributive
- Identity
6. Commutative Property states that -
- a+b = b+a
- a*b=b *a
- Both A and B
- None of the above
Answer: C) Both A and B
Explanation:
Commutative Property states that -
- a+b = b+a
- a*b=b *a
7. Distributive Property states that -
- a+(b*c)=(a+b)*(a+c)
- a*(b+c)=(a*b)+(a*c)
- Both A and B
- None of the above
Answer: C) Both A and B
Explanation:
Distributive Property states that -
- a+(b*c)=(a+b)*(a+c)
- a*(b+c)=(a*b)+(a*c)
8. Identity Property states that -
- a+0=a
- a *1=a
- Both A and B
- None of the above
Answer: C) Both A and B
Explanation:
Identity Property states that -
- a+0=a
- a *1=a
9. Complemented Laws states that -
- a+a'=1
- a * a'=0
- Both A and B
- None of the above
Answer: C) Both A and B
Explanation:
Complemented Laws states that -
- a+a'=1
- a * a'=0
10. If A itself is a Boolean Algebra, then (A,*, +,', 0,1) is a ____ of B.
- Sub-algebra
- Sub-Boolean Algebra
- Both A and B
- 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.
11. Subsets of a Boolean Algebra can be ____, but may or may not be subalgebras because B may not be closed.
- Algebra
- Boolean Algebra
- Sub-algebra
- 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.
- Isomorphic
- Boolean Functions
- Boolean Expressions
- 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?
- f (a+b)=f(a)+f(b)
- f (a*b)=f(a)*f(b)
- f(a')=f(a)'
- All of the above
Answer: D) All of the above
Explanation:
The following are Isomorphic-Boolean Algebras -
- f (a+b)=f(a)+f(b)
- f (a*b)=f(a)*f(b)
- f(a')=f(a)'
14. Which of the following is/are the basic property/ies of Boolean Algebra?
- Idempotent Law
- Commutative Property
- Associative Property
- All of the above
Answer: D) All of the above
Explanation:
The following are the properties of Boolean Algebra -
- Idempotent Law
- Commutative Property
- Associative Property
15. Which of the following is/are NOT the basic property/ies of Boolean Algebra?
- Absorption Laws
- Identity Laws
- Null Laws
- Evolution Laws
Answer: D) Evolution Laws
Explanation:
Evolution Laws is NOT the basic property of Boolean Algebra.
16. Which of the following statement is TRUE?
- 0 ≤ a ≤ 1 ∀ a ∈ B.
- There is a unique complement b' for every element b.
- Both A and B
- None of the above
Answer: C) Both A and B
Explanation:
The following statements are TRUE -
- 0 ≤ a ≤ 1 ∀ a ∈ B.
- 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 ____.
- Algebra
- Expression
- Function
- 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.
- Tabular
- Graphical
- Analytical
- None
Answer: A) Tabular
Explanation:
Tabular descriptions of functions are always possible.
19. ____ can be used as an alternative method of expressing functions.
- Function
- Expression
- Law
- 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.
- [0, 1]2 to [0, 1]
- [0, 1]3 to [0, 1]
- [0, 1]n-1 to [0, 1]
- [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.