# Switching Circuits Questions and Answers – Boolean Algebra Simplification Theorems

This set of Switching Circuits Multiple Choice Questions & Answers (MCQs) focuses on “Boolean Algebra Simplification Theorems”.

1. The Boolean expression A.B + A.B’ is equal to A .
a) True
b) False

Explanation: The steps to derive the solution are given below.
A.B + A.B’
= A.(B + B’)
= A.(1)   (Because B + B’ = 1)
= A.

2. The Boolean expression (A + B)(A + B’) is equal to A.
a) True
b) False

Explanation: The steps to derive the solution are given below.
A.A + B.A + A.B’ + B.B’
= A +A.(B + B’)   (Because B.B’ = 0)
= A + A   (Because B + B’ = 1)
= A

3. Simplify the Boolean expression A + A.B.
a) A
b) B
c) A’
d) A.B

Explanation: The steps to derive the solution are given below.
A + A.B
= A.1 + A.B
= A.(1 + B)
= A.1  (Because 1 + B = 1)
= A.

4. Simplify the Boolean expression A.(A + B).
a) A
b) B
c) A’
d) A.B

Explanation: The steps to derive the solution are given below.
A.(A + B)
= A.A + A.B
= A.(1 + B)   (Because A.1 = A)
= A.1  (Because 1 + B = 1)
= A

5. Simplify the Boolean expression A + A’.B.
a) A + B
b) A + B’
c) (A.B)’
d) A’.B

Explanation: The steps to derive the solution are given below.
A + A’.B
= (A + A’).(A + B)
= 1.(A + B)  (Because A + A’ = 1)
= A + B

6. Simplify the Boolean expression A.(A’ + B).
a) A.B
b) A.B’
c) A + B’
d) A’ + B

Explanation: The steps to derive the solution are given below.
A.(A’ + B)
= A.A’ + A.B
= 0 + A.B  (Because A.A’ = 0)
= A.B

7. Simplify the Boolean expression A.B + A′.C + B.C.
a) A.B + C
b) B.(A + C)
c) A.B + A’.C
d) A.B + C’

Explanation:The steps to derive the solution are given below.
A.B + A′.C + B.C
= A.B + A′.C + (1).B.C
= A.B + A′.C + (A + A′).B.C   (Because A + A’ = 1)
= A.B + A.B.C + A′.C + A′.B.C
= A.B + A’.C

8. Simplify the Boolean expression (A + B).(A’ + C).(B + C).
a) A.C + B
b) (A + B)(A’ + C)
c) A.B + C
d) A.B.C’

Explanation: The validity of the boolean equation (A + B).(A’ + C).(B + C) = (A + B)(A’ + C) can be verified by the following truth table.

A B C A+B A’+C B+C (A+B).(A’+C).(B+C) (A+B)(A’+C)
0 0 0 0 1 0 0 0
0 0 1 0 1 1 0 0
0 1 0 1 1 1 1 1
0 1 1 1 1 1 1 1
1 0 0 1 0 0 0 0
1 0 1 1 1 1 1 1
1 1 0 1 0 1 0 0
1 1 1 1 1 1 1 1

Sanfoundry Global Education & Learning Series – Switching Circuits.