Question $1.$ Optimize the following Boolean functions F together with the don$$t care conditions d$.$ Find all prime

implicants and essential prime implicants, and apply the selection rule. $[10$ marks$]$

$($a$)$ F$($A$,$ B$,$ C$)=\backslash$Sigma m $(3,5,6),$ d$($A$,$ B$,$ C$)=\backslash$Sigma m $(0,7)$

$($b$)$ F$($W$,$ X$,$ Y$,$ Z$)=\backslash$Sigma m $(0,2,4,5,8,14,15),$ d$($W$,$ X$,$ Y$,$ Z$)=\backslash$Sigma m $(7,10,13)$

Question $2.$ Optimize the following Boolean functions F together with the don$$t care conditions d in

$($a$)$ sum$-$ of$-$ products and $($b$)$ product$-$ of$-$ sums form: $[10$ marks$]$

F$($W$,$ X$,$ Y$,$ Z$)=\backslash$Sigma m $(5,6,11,12),$ d$($W$,$ X$,$ Y$,$ Z$)=\backslash$Sigma m $(0,1,2,9,10,14,15)$