Derive the complement function of : $(10)$

$F(A,B,C,D)=(3,6,8,10,14)$

Optimize the following Boolean Algebra

a$.F(x,Y,Z)={\displaystyle \underset{?}{\overset{?}{}}}(2,3,4,7)$

b$.F(x,Y,Z)=(0,4,5,6)$

c$.F(A,B,C)=(0,2,4,6,7)$

d$.F(A,B,C)={\displaystyle \underset{?}{\overset{?}{}}}(0,1,3,4,6,7)$

Optimize the following Boolean Algebra using a map:

a$.F=x^{\text{'}}{Z}^{\text{'}}+Y{Z}^{\text{'}}+xYZ$

b$.F=A^{\text{'}}B+B^{\text{'}}C+A^{\text{'}}{B}^{\text{'}}{C}^{\text{'}}$

c$.F=A^{\text{'}}{B}^{\text{'}}+A{C}^{\text{'}}+B^{\text{'}}C+A^{\text{'}}B{C}^{\text{'}}$