# Switching Circuits Questions and Answers – Commutative, Associative and DeMorgan’s Laws

This set of Switching Circuits Multiple Choice Questions & Answers (MCQs) focuses on “Commutative, Associative and DeMorgan’s Laws”.

1. The AND operation is commutative.
a) True
b) False

Explanation: The answer to the above question can be verified using the following truth table.

A B A.B B.A
0 0 0 0
0 1 0 0
1 0 0 0
1 1 1 1

From the above truth table, it can be verified that A.B = B.A. Hence, the AND operation is commutative.

2. The OR operation is commutative.
a) True
b) False

Explanation: The answer to the above question can be verified using the following truth table.

A B A+B B+A
0 0 0 0
0 1 1 1
1 0 1 1
1 1 1 1

From the above truth table, it can be verified that A+B = B+A. Hence, the OR operation is commutative.

3. Which among the below Boolean expressions is equal to (A.B).C?
a) A + B + C
b) A.(B.C)
c) A + B.C
d) A.C + B

Explanation: The answer to the above question can be verified using the following truth table.

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

From the above table it can be verified that (A.B).C = A.(B.C). Thus, the AND operation has associative property.

4. Which among the below Boolean expressions is equal to (A + B) + C?
a) A.B + C
b) A + (B + C)
c) A + B.C
d) A.C + B

Explanation: The answer to the above question can be verified using the following truth table.

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

From the above table it can be verified that (A + B) + .C = A + (B + C). Thus, the OR operation has associative property.

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

Explanation: The answer to the above question can be verified using the following truth table.

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

From the above table it can be verified that (A + B)’ = A’.B’. Thus, DeMorgan’s law is verified.

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

Explanation: The answer to the above question can be verified using the following truth table.

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

From the above table it can be verified that (A.B)’ = A’ + B’. Thus, DeMorgan’s law is verified.

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

Explanation: The answer to the above question can be verified using the following truth table.

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

From the above table it can be verified that A.(B + C) = A.B + A.C. Thus, the first Distributive Law of Boolean Algebra is verified.

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

Explanation: The answer to the above question can be verified using the following truth table.

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

From the above table it can be verified that A + B.C = (A +B).(A+C). Thus, the second Distributive Law of Boolean Algebra is verified.

9. Which operation is the dual of AND operation?
a) OR
b) NOR
c) NOT
d) NAND

Explanation: The dual of a Boolean Algebra expression is obtained by interchanging the constants 0 and 1 and interchanging the operations of AND and OR. Variables and complements are left unchanged. The dual of AND is OR and the dual of OR is AND.

Sanfoundry Global Education & Learning Series – Switching Circuits.

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