Problem $2)$ Optimize the following Boolean functions by means of $4-$variable k$-$map

a$)F(A,B,C,D)={\displaystyle \underset{?}{\overset{?}{}}}$ of $(m2,m3,m8,m9,m10,m12,m13,m14)$

b$)F(A,B,C,D)={\displaystyle \underset{?}{\overset{?}{}}}$ of $(m1,m3,m6,m7,m9,m11,m12,m13,m15)$

Problem $3)$ Express F in Problem $2$ in term of POS.

Problem $4)$ Find the truth table for the following function $F.$

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