# Discrete Mathematics Questions and Answers – Boolean Algebra

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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

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

Explanation: For designing 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–>Yk
b) A special mathematical function with n degrees such that f:Yn–>Y
c) An algebraic function with n degrees such that f:Xn–>X
d) A polynomial function with k degrees such that f:X2–>Xn

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

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

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

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

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

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

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.
b) product
c) moduler
d) subtraction

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

Sanfoundry Global Education & Learning Series – Discrete Mathematics.

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