$(20$ points$)$ The Pull$-$Down Network $($PDN$)$ is provided for the CMOS logic gate below.

a$)(10)$ Sketch the equivalent pull up network $($PUN$))$

b$)(10)$ Circle the logic function that describes the behavior of the gate? $($circle one$)$

$\frac{?}{\text{b}\text{a}\text{r}}(AB(C+D))\frac{,}{b}ar((A+B)CD)\frac{,}{b}ar\frac{A}{b}ar(B)\frac{+}{b}ar\frac{C}{b}ar(D)\frac{,}{b}ar(A+B+CD)$