Properties of Boolean Algebra Practice Questions

Properties of boolean algebra are the basic rules or laws used to simplify Boolean expressions. They make logical expressions easier to understand, solve, and implement in digital circuits.

Example: A + 0 = A and A · 1 = A

These rules help reduce complex Boolean expressions into simpler forms.

Question 1: Simplify A . B + A . B'.

Solution:

A . B + A . B' = A . (B + B')

= A . (1)

= A

Question 2: Simplify A + A' . B.

Solution:

A + A' . B = (A + A') . (A + B)

= (1) . (A + B)

= A + B

Question 3: Simplify (A + B) . (A + B') + (B . B').

Solution:

(A + B) . (A + B') + (B . B') = (A + B) . (A + B') + (0)

A + (B . B')

= A + (0)

= A

Question 4: Simplify A . (B + C) + A' . (B + C)

Solution:

A . (B + C) + A' . (B + C) = (A + A') . (B + C)

= 1 . (B + C)

= B + C

Question 5: Simplify A + B . A' + C . C'

Solution:

A + B . A' + C . C' = A + B . A' + 0

= A + B

Unsolved Questions

Question 1: Simplify A + A.B
Question 2: Simplify (A.B) + (A.B') + (B.B')
Question 3: Simplify A + B + A'.B
Question 4: Simplify (A.B) + (A.B') + (A'.B)
Question 5: Simplify A + B + A.B