a$)$ Use a truth table to demonstrate the validity of $x+yz=(x+y)(x+z)$

b$)$ Simplify to a minimum number of literals $xyz+x^{\text{'}}y+xyz$

c$)$ Simplify to a minimum number of literals $(x+y{)}^{\text{'}}(x^{\text{'}}+y^{\text{'}}{)}^{\text{'}}$

d$)$ Reduce the following to $3$ literals $(x^{\text{'}}{y}^{\text{'}}+z{)}^{\text{'}}+z+xy+wz$

e$)$ Draw the original circuit for part c$.$