Question

What should be the output of the following boolean expression after simplifying it to a minimum number of variables? \[ a'b' + ab + a'b \]

• A. \( a + b' \)
• B. \( a' + b \)
• C. \( a'b' + b \)
• D. \( a + b \)

Hint:

The **absorption law** simplifies expressions such as \( a' + ab = a + b \).

Answer 1

The Correct Option is D

The provided boolean expression is:\[ a'b' + ab + a'b \]Simplification process:- Grouping the terms: \( a'b' + ab + a'b = a'(b' + b) + ab \)- Applying the complement law \( b' + b = 1 \): \( a' \cdot 1 + ab = a' + ab \)- Applying the absorption law: \( a' + ab = a + b \).The simplified expression is:\[ a + b \]Therefore, the correct output is (4) \( a + b \).