$(15$ points$)$ Simplify the following Boolean functions using the three$-$variable Karnaugh map format provided in 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$)F(x,y,z)=(1,2,4,6,7)$