For the following boolean function:

F$=$xy$\text{'}$z $+$x$\text{'}$y$\text{'}$z$+$w$\text{'}$xy$+$wx$\text{'}$y$+$wxy

a$)$ draw the logic gates diagram, using the original boolean expression

b$)$ use boolean algebra to simplify the functions to a minimum number of literals

c$)$ draw the logic diagram from the simplified expression and compare the total number of gates with the diagram of part a$)$