Part $1$:

Diagram the following problems by using Boolean algebra

$x=AB+A(B+C)+B(B+C)$

$Y=A^{\text{'}}{B}^{\text{'}}{C}^{\text{'}}+A^{\text{'}}{B}^{\text{'}}C+A{B}^{\text{'}}{C}^{\text{'}}+A{B}^{\text{'}}C$