verify each of the identities below using algebraic manipulation. $($That is$,$ transform one side of the equation into the other using Boolean Algebra.$)(2$ points$)$ ab $+$ a c $+$ b c $=$ abc $+$ c $(2$ points$)($x $+$ y $)($ x $+$ z$)=$ x $+$ x y z $(2$ points$)($x $+$ y $+$ z$)($x $+$ y $+$ z$)=$ x $+$ y $(3$ points$)($a $+$ c$)($a $+$ b$)($b $+$ c$)=($a $+$ c $+$ b$)$b $(3$ points$)$ x y $+$ yz $+$ xz $=$ x y $+$ xz