$(20$ points$)$ Simplify the following functions using K$-$Maps to the minimum SOPs:

$($a$)F=C^{\text{'}}D+AB{C}^{\text{'}}+AB{D}^{\text{'}}+A{B}^{\text{'}}{D}^{\text{'}}$

$($b$)F=(A^{\text{'}}+B+D^{\text{'}})(A^{\text{'}}+B^{\text{'}}+C^{\text{'}})(A^{\text{'}}+B^{\text{'}}+C)(B^{\text{'}}+C+D^{\text{'}})$

$($c$)F(x,y,z,w)=$prod$(1,3,5,7,13,15)$

$($d$)F(x,y,z,w)={\displaystyle \underset{m}{\overset{?}{}}}(0,6,8,13,14)+{\displaystyle \underset{d}{\overset{?}{}}}(2,4,10)$