Consider the combinational circuit shown in Figure Q$1.$

$($a$)$ Derive the Boolean expressions for $T_1$ through $T_4.$ Express the output $F$ as a function of the four inputs.

$($b$)$ List the truth table with $16$ binary combinations of the four input variables. Then give the binary values for

$T_1$ through $T_4$ and output $F$ in the table.

$($c$)$ Plot the output Boolean function obtained in part $($b$)$ on a k$-$map and find a simplified Boolean expression

and implement it using two$-$input inverting gates only.