Simplify the following Boolean phrases by using the Boolean basic algebra statements

Question

Simplify the following Boolean phrases by using the Boolean basic algebra statements:

$(ac)+(bc)+(!ab)$ to the expression $(ac)+(!ab)$.

Answer 1

From $$BC=(A+A')BC=ABC+A'BC=(AC+A'B)BC,$$ we get \begin{align} AC+BC+A'B &=AC+BC(AC+A'B)+A'B\\ &=AC(1+BC)+A'B(1+BC)\\ &=AC+A'B. \end{align}