Boolean Algebraic Theorems Practice Questions

Last Updated : 8 Jul, 2026

Boolean algebraic theorems are a set of proven rules used to simplify Boolean expressions without changing their output. These theorems define how the Boolean operators AND (·), OR (+), and NOT (') work with the binary values 0 and 1, making logic expressions easier to understand and digital circuits simpler to design.

Example: In the expression, A + 0 = A

Solution:

Using the Identity Theorem:

If A = 0:
LHS = 0 + 0 = 0 = RHS

If A = 1:
LHS = 1 + 0 = 1 = RHS

Hence, A + 0 = A is proved.

Question 1: Using De Morgan's Theorem, simplify the Boolean expression: F = (A + B)'.

Solution:

Given, F = (A + B)'

Using De Morgan's Theorem,

(A + B)' = A'B'

Therefore,

F = A'B'

Question 2: Find the dual of the Boolean expression: F = A + 0.

Solution:

Given, F = A + 0

Using the Duality Theorem, replace every:

  • + with .
  • 0 with 1

Therefore, F = A . 1

Question 3: Simplify the Boolean expression: F = (A')'

Solution:

Given, F = (A')'

Using the Inversion Law,

(A')' = A

Therefore, F = A

Question 4: Using the Commutative and Associative Laws, rewrite the Boolean expression so that similar terms are grouped together. F = C + A + B + A.C

Solution:

Given, F = C + A + B + AC

Using the Commutative Law, rearrange the terms.

F = A + AC + B + C

Now the related terms are grouped together.

Using the Redundancy Theorem,

A + AC = A

Therefore, F = A + B + C.

Question 5: Using Boolean theorems, prove that the following expression is always equal to 1. F = (A + B)(A' + B')

Solution:

Given, F = (A + B)(A' + B')

Apply the Distributive Law.

F = AA' + AB' + BA' + BB'

Using the Complementary Theorem,

AA' = 0

BB' = 0

Therefore, F = AB' + A'B.

Question 6: Which Boolean theorem is most appropriate for simplifying each of the following expressions?

  1. (A + B)'
  2. (A')'
  3. A + AB
  4. A(B + C)

Solution:

  • (A + B)' → De Morgan's Theorem
  • (A')' → Inversion Law
  • A + AB → Redundancy (Absorption) Theorem
  • A(B + C) → Distributive Law.

Practice Questions

Question 1: Simplify the Boolean expression using De Morgan's Theorem: F = (AB)'

Question 2: Find the dual of the Boolean expression: F = A . 0

Question 3: Using the Distributive Law, expand the Boolean expression: F = A(B + C + D)

Question 4: Verify whether the following expression satisfies the Complementary Theorem: F = A + A'

Question 5: Rewrite the following Boolean expression using the Commutative and Associative Laws: F = C.A + B + A + C

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