$f(a,b,c,d)={\displaystyle \underset{?}{\overset{?}{}}}(0,9,10,12,13)+{\displaystyle \underset{?}{\overset{?}{}}}(2,6,8,14)$

A logical function is given as follows

a$)$ Simplify this function into Sum of Products $($SOP$)$ form using a Karnaugh map. Implement the simplified expression using only NOR gates.

b$)$ Simplify this function into Product of Sums $($POS$)$ form. Implement the simpliffed expression using only NAND gates.

c$)$ Compare the designs from parts a$)$ and b$)$ in terms of design criteria. Explain which design would be a more sultable choice and why.