Question

example 3
$(a+b)(a+\overline{b})$

Explanation:

Step1: Expand using distributive property

$(A+B)(A+\overline{B}) = A\cdot A + A\cdot\overline{B} + B\cdot A + B\cdot\overline{B}$

Step2: Simplify boolean products

$A\cdot A = A$, $B\cdot\overline{B}=0$, $A\cdot\overline{B}+A\cdot B = A(\overline{B}+B)$

Step3: Simplify boolean sum

$\overline{B}+B=1$, so $A\cdot1 = A$

Answer:

$A$