$1.$ Simplify the following Boolean function using a K$-$map. You must show the K$-$map and indicate your groupings to show how you arrived at the simplified function. $(15$ pts$)$

F$($x$,$y$,$z$)=$ x$\text{'}$y$\text{'}$z $+$ x$\text{'}$y$\text{'}$z$\text{'}+$ x$\text{'}$yz$\text{'}+$ xy$\text{'}$z$\text{'}+$ xyz$\text{'}$