answer all of them and explain each process: Do the following problems: $2.$a$.$Given the function from Boolean logic, F $($x$,$ y$,$ z$)=($y$($x$$z $+$ xz$)+$ x$($yz $+$ yz$))($ y$($x$$z $+$ xz$)+$ x$($yz $+$ yz$)),$ Create the truth table for F$().$ Then draw the logic diagram using the original Boolean expression. Then simplify the logic expression using identities or laws from Boolean algebra. $2.$b$.$Implement the XOR$($x$,$y$)$ Boolean logic function using just the AND$(.,.),$ OR$(.,.)$ and NOT$(.)$ functions. $2.$c$.$Any two$-$argument L$($x$,$y$)$ Boolean function can be implemented using just AND, OR and NOT Boolean functions. Take this as given. $($Extra Credit: Prove, or demonstrate this by construction.$)2.$d$.$ Show that the NAND$($x$,$y$)$ function can be used as a universal logic gate function, by implementing each of AND, OR and NOT Boolean functions, using just the NAND function. $2.$e$.$Show that the NOR$($x$,$y$)$ function case be used as a universal logic gate function, by implementing each of AND, OR and NOT Boolean functions, using just the NOR function.