Consider the following function: F$($w$,$ x$,$ y$,$ z$)=(0,2,4,6,8,9,10,11,12).$

Use the k$-$map to:a$)$ Simplify the function into SOP expression and then implement it using NAND

gates only.

b$)$ Simplify the function into POS expression and then implement it using NOR gates

only.