For the $3$ Boolean Functions below.

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

$Z=(B+C^{\text{'}})(B^{\text{'}}+C)+(A^{\text{'}}+B+C^{\text{'}}{)}^{\text{'}}$

$x=(C+D{)}^{\text{'}}+A^{\text{'}}C{D}^{\text{'}}+A{B}^{\text{'}}{C}^{\text{'}}+A^{\text{'}}{B}^{\text{'}}CD+AC{D}^{\text{'}}$

a$.$ Simplify the functions using boolean algebra to show that

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

$Z=BC+B^{\text{'}}(C^{\text{'}}+A)$

$x=D^{\text{'}}+A{B}^{\text{'}}{C}^{\text{'}}+A^{\text{'}}{B}^{\text{'}}C$