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Discrete Mathematics | Boolean Expressions MCQs

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

1. In Boolean algebra B, a Boolean expression is defined as -

1. The elements of B are all Boolean expressions.
2. Boolean expressions are used to name variables.
3. If a₁ and a₂ are Boolean expressions, then a₁,'∨ a₂ and a₁∧ a₂ are Boolean expressions.
4. All of the above

Answer: D) All of the above

Explanation:

In Boolean algebra B, a Boolean expression is defined as -

1. The elements of B are all Boolean expressions.
2. Boolean expressions are used to name variables.
3. If a₁ and a₂ are Boolean expressions, then a₁,'∨ a₂ and a₁∧ a₂ are Boolean expressions.

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2. Boolean expressions containing n distinct variables are normally referred to as Boolean ____ of n variables.

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

Answer: C) Expressions

Explanation:

Boolean expressions containing n distinct variables are normally referred to as Boolean expressions of n variables.

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3. The Boolean Expression E (x₁,x₂,....x_n) is a set of n variables over a Boolean algebra B. An assignment of values to variables x₁, x₂, ... x_n means assigning elements of A as variables' values. ____ the variables in the expression by their values will allow us to evaluate E ( x₁, x₂, .... x_n).

1. Adding
2. Subtracting
3. Multiplying
4. Substituting

Answer: D) Substituting

Explanation:

The Boolean Expression E (x₁,x₂,....x_n) is a set of n variables over a Boolean algebra B. An assignment of values to variables x₁, x₂, ... x_n means assigning elements of A as variables' values. Substituting the variables in the expression by their values will allow us to evaluate E ( x₁, x₂, .... x_n).

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4. When n variables are assigned the same value for every assignment, two Boolean expressions are said to be _____.

1. Equal
2. Unequal
3. Zero
4. Similar

Answer: A) Equal

Explanation:

When n variables are assigned the same value for every assignment, two Boolean expressions are said to be equal.

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5. ____ indicates that E₁( x₁,x₂,....x_n) and E₂( x₁,x₂,....x_n) are equivalent.

1. E₁( x₁,x₂,....x_n)+E₂( x₁,x₂,....x_n)
2. E₁( x₁,x₂,....x_n)-E₂( x₁,x₂,....x_n)
3. E₁( x₁,x₂,....x_n)=E₂( x₁,x₂,....x_n)
4. E₁( x₁,x₂,....x_n)!=E₂( x₁,x₂,....x_n)

Answer: C) E₁( x₁,x₂,....x_n)=E₂( x₁,x₂,....x_n)

Explanation:

E₁( x₁,x₂,....x_n)=E₂( x₁,x₂,....x_n) indicates that E₁( x₁,x₂,....x_n) and E₂( x₁,x₂,....x_n) are equivalent.

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6. A Boolean Expression composed of n variables is a ____ if it follows the form x̅₁∧x̅₂∧x̅₃∧....∧x̅_n where x_i is used to denote x_i or x_i'.

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

Answer: B) Min-term

Explanation:

A Boolean Expression composed of n variables is a min-term if it follows the form x̅₁∧x̅₂∧x̅₃∧....∧x̅_n where x_i is used to denote x_i or x_i'.

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