$(3)(5$ marks$)$ Find the complement for each of the following Boolean functions:

$[$Must show the intermediate conversion steps$]$

a$)(a+c)*(a\frac{+}{b}ar(b))*(+b\frac{+}{b}ar(c))$

b$)z\frac{+}{b}ar(z)*(\frac{?}{\text{b}\text{a}\text{r}}(v)*w+x*y)$

$(4)(10$ marks$)$ Draw the logic circuit for the following Boolean function:

$[$Must show the intermediate conversion steps$]$

$F=x*y+\stackrel{}{x}\frac{*}{b}ar(y)\frac{+}{b}ar(y)*z$

a$)$ With NAND and Inverter gates $[$You may use one$-$three input NAND gate$]$

b$)$ With NOR and Inverter gates $[$You may use one$-$three input NOR gate$]$