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 given boolean expression is: \[ a'b' + ab + a'b \] Let's simplify it step-by-step: - First, notice that the expression can be grouped as follows: \[ a'b' + ab + a'b = a'(b' + b) + ab \] - From the **complement law**: \( b' + b = 1 \), so the expression becomes: \[ a' \cdot 1 + ab = a' + ab \] - Now, we use the **absorption law**: \( a' + ab = a + b \). Thus, the simplified expression is: \[ a + b \] Hence, the correct output is **(4) \( a + b \)**.