$($a$)$ Using Boolean theorems and laws show that the Boolean function

$f(x,Y,Z)=(x+Y)(x^{\text{'}}+Z)Z^{\text{'}}{Y}^{\text{'}}+x(Y+Z)+(ZYx+Y)(ZYx+xZ)$ can be

simplified to $x(Y+Z).$

$($b$)$ Show that the simplification process in part $($a$)$ has significantly reduced the

number of logic gates required to implement the expression. Include the following in

your answer:

Draw the two networks $($network for the original expression and network for

the reduced expression$)$ using only $2-$input AND and OR gates. Assume that

complemented $($inverted$)$ variables are available i$.$e$.$ no need to use inverters.

You should not attempt to simplify the expressions, but you should reuse

gates, if possible. The diagrams must be neat enough for the marker to

understand and grade them.

Mention how many gates have been "saved" by this simplification.

$1$ point