Using K$-$map, simplify the following Boolean functions as follows

$$

Draw a K$-$map for the function: Answer not provided

Find all prime implicants $($PI$$s$).$ Mark on the K$-$map and write the Boolean expression of the PI$.$

Answer: All PI's:$$ w$\text{'}$x$\text{'},$ wxy$,$ x$\text{'}$y$\text{'}$z$,$ xy$\text{'}$z$\text{'},$ w$\text{'}$y$\text{'}$

Indicate essential PI$$s $($mark with $*)$

Answer: All EPI's:$$ w$\text{'}$x$\text{'},$ wxy$,$ x$\text{'}$y$\text{'}$z

Find the simplified expression $($if more than one optimum solution is found, list all of them$).$

Answer: F$($w$,$ x$,$ y$,$ z$)=$ w$\text{'}$x$\text{'}+$ wxy $+$ x$\text{'}$y$\text{'}$z $+$ w$\text{'}$y$\text{'}$