$(20$ Points$)5\mathrm{.}20($b$),($c$)$

Use Karnaugh maps to find all possible minimum sum$-$of$-$products expressions for each function.

$($b$)g(d,e,f)=m(1,4,6)+d(0,2,7)$

$($c$)F(p,q,r)=(p+q^{\text{'}}+r)(p^{\text{'}}+q+r^{\text{'}})$