This set of Discrete Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Boolean Algebra”.

1. Algebra of logic is termed as ______________

a) Numerical logic

b) Boolean algebra

c) Arithmetic logic

d) Boolean number

View Answer

Explanation: The variables that can have two discrete values False(0) and True(1) and the operations of logical significance are dealt with Boolean algebra.

2. Boolean algebra can be used ____________

a) For designing of the digital computers

b) In building logic symbols

c) Circuit theory

d) Building algebraic functions

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Explanation: For designing of the digital computers and building different electronic circuits boolean algebra is accepted widely.

3. What is the definition of Boolean functions?

a) An arithmetic function with k degrees such that f:Y–>Y^{k}

b) A special mathematical function with n degrees such that f:Y^{n}–>Y

c) An algebraic function with n degrees such that f:X^{n}–>X

d) A polynomial function with k degrees such that f:X^{2}–>X^{n}

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Explanation: A Boolean function is a special mathematical function with n degrees and where Y = {0,1} is the Boolean domain with being a non-negative integer. It helps in describing the way in which the Boolean output is derived from Boolean inputs.

4. F(X,Y,Z,M) = X`Y`Z`M`. The degree of the function is ________

a) 2

b) 5

c) 4

d) 1

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Explanation: This is a function of degree 4 from the set of ordered pairs of Boolean variables to the set {0,1}.

5. A ________ value is represented by a Boolean expression.

a) Positive

b) Recursive

c) Negative

d) Boolean

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Explanation: A Boolean value is given by a Boolean expression which is formed by combining Boolean variables and logical connectives.

6. Which of the following is a Simplification law?

a) M.(~M+N) = M.N

b) M+(N.O) = (M+N)(M+O)

c) ~(M+N) = ~M.~N

d) M.(N.O) = (M.N).O

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Explanation: By Simplification Law we can have X.(~X+Y) = X.Y and X+(~X.Y) = X+Y. By, De’ Morgan’s law ~(X+Y) = ~X.~Y. By commutative law we can say that A.(B.C) = (A.B).C.

7. What are the canonical forms of Boolean Expressions?

a) OR and XOR

b) NOR and XNOR

c) MAX and MIN

d) SOM and POM

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Explanation: There are two kinds of canonical forms for a Boolean expression-> 1)sum of minterms(SOM) form and

2)product of maxterms(SOM) form.

8. Which of the following is/are the universal logic gates?

a) OR and NOR

b) AND

c) NAND and NOR

d) NOT

View Answer

Explanation: NAND and NOR gates are known as the universal logic gates. A universal gate is a gate which can implement any Boolean function without the help of 3 basic gate types.

9. The logic gate that provides high output for same inputs ____________

a) NOT

b) X-NOR

c) AND

d) XOR

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Explanation: The logic gate which gives high output for the same inputs, otherwise low output is known as X-NOR or Exclusive NOR gate.

10. The ___________ of all the variables in direct or complemented from is a maxterm.

a) addition

b) product

c) moduler

d) subtraction

View Answer

Explanation: The Boolean function is expressed as a sum of the 1-minterms and the inverse of function is represented as 0-minterms.

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