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Discrete Mathematics | Canonical Forms MCQs

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

1. How many types of canonical forms are there?

1. 2
2. 3
3. 4
4. 5

Answer: A) 2

Explanation:

2 types of canonical forms are there.

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2. Which of the following is/are the canonical form(s)?

1. Disjunctive Normal Forms
2. Conjunctive Normal Forms
3. Both A and B
4. None of the above

Answer: C) Both A and B

Explanation:

The following are the canonical forms -

1. Disjunctive Normal Forms
2. Conjunctive Normal Forms

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3. Disjunctive Normal Forms are also known as -

1. Sum of Products
2. SOP
3. Both A and B
4. None of the above

Answer: C) Both A and B

Explanation:

Disjunctive Normal Forms are also known as -

1. Sum of Products
2. SOP

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4. When A Boolean expression over ({0, 1}, ∨,∧,') is a join of min-terms, it is said to be in ____ normal form.

1. Conjunctive
2. Disjunctive
3. Both A and B
4. None of the above

Answer: B) Disjunctive

Explanation:

When A Boolean expression over ({0, 1}, ∨,∧,') is a join of min-terms, it is said to be in disjunctive normal form.

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5. A Boolean Expression composed of n variables is a ______ if it follows the form x₁∨x₂∨..........∨x_n where x_i is used to denote x_i or x_i'.

1. Min-term
2. Max-term
3. Mode-term
4. Median-term

Answer: B) Max-term

Explanation:

A Boolean Expression composed of n variables is a max-term if it follows the form x₁∨x₂∨..........∨x_n where x_i is used to denote x_i or x_i'.

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6. Conjunctive Normal Forms are also known as -

1. Product of Sums
2. POS
3. Both A and B
4. None of the above

Answer: C) Both A and B

Explanation:

Conjunctive Normal Forms are also known as -

1. Product of Sums
2. POS

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7. Conjunctive normal form of a Boolean expression over ({0, 1}, ∨,∧,') is when a Boolean expression meets ____.

1. Max-terms
2. Min-terms
3. Mode-terms
4. Median-terms

Answer: A) Max-terms

Explanation:

Conjunctive normal form of a Boolean expression over ({0, 1}, ∨,∧,') is when a Boolean expression meets max-terms.

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8. In disjunctive normal forms, a Boolean expression corresponding to a function from {0, 1}ⁿ to {0, 1} can be obtained by having a min-term for each ordered n-tuple of 0's and 1's in which the function is ____.

1. 1
2. 0
3. 2
4. N

Answer: A) 1

Explanation:

In disjunctive normal forms, a Boolean expression corresponding to a function from {0, 1}ⁿ to {0, 1} can be obtained by having a min-term for each ordered n-tuple of 0's and 1's in which the function is 1.

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9. For each ordered n-tuple of 0's and 1's for which the value of function is ____, a Boolean expression can be obtained in conjunctive normal forms.

1. 0
2. 1
3. Null
4. 2

Answer: A) 0

Explanation:

For each ordered n-tuple of 0's and 1's for which the value of function is 0, a Boolean expression can be obtained in conjunctive normal forms.

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10. When the identity elements 0 and 1, in the original expression E, are switched, then the ____ of that expression is obtained.

1. Dual
2. Duplex
3. Triplet
4. Identity

Answer: A) Dual

Explanation:

When the identity elements 0 and 1, in the original expression E, are switched, then the dual of that expression is obtained.

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11. The duals of any theorem in a Boolean algebra are also ____.

1. Theorems
2. Functions
3. Expressions
4. Laws

Answer: A) Theorems

Explanation:

The duals of any theorem in a Boolean algebra are also theorems.

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12. A Boolean Expression composed of n variables is a ______ if it follows the form x₁∨x₂∨..........∨x_n where x_i is used to denote x_i or x_i'.

1. Min-term
2. Max-term
3. Mode-term
4. Median-term

Answer: B) Max-term

Explanation:

A Boolean Expression composed of n variables is a max-term if it follows the form x₁∨x₂∨..........∨x_n where x_i is used to denote x_i or x_i'.

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