$1.(15$ points$)$ Simplify the following Boolean functions using the three$-$variable Karnaugh map format providedin Figure $2.($a$)(5$ points$)$ F$($x$,$ y$,$ z$)=(1,2,3)($b$)(5$ points$)$ F$($x$,$ y$,$ z$)=(1,3,4,6)($c$)(5$ points$)$ F$($x$,$ y$,$ z$)=(1,2,4,6,7)$