$14.$ Simplify the following functional expressions using Boolean algebra and its identities. List the identity used at each step.

a$)$ F$($x$,$y$,$z$)=$ y$($x$\text{'}+($x $+$ y$)\text{'})$

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

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

$$

$23.$ The truth table for a Boolean expression is shown below. Write the Boolean expression in sum$-$of$-$products form.