Consider the Boolean function F$($w$,$x$,$y$,$z$)=$ wxz $+$ xy$+$ w$$x $+$ wx$$yz$+$ xy$.(30$ points$)$ a$)$ Simplify F to a minimum number of literals using Boolean Algebra. b$)$ Implement the simplified result obtained in $$a$)$ assuming variables and their complements are available: $($i$)$ as a SOP, $($ii$)$ as a POS, $($iii$)$ as NAND$-$only, $($iv$)$ as NOR$-$only.