Complete the following exercises for combinational logic design and show your work. $($a$)$ Complete a truth table that has $3$ inputs $($A$,$ B$,$ and C$)$ and one output $($F$).$ F is asserted $(1)$ whenever both B and C are deasserted $(0).$ F is asserted $(1)$ whenever A is deasserted $(0).$ F is deasserted $(0)$ in all other cases. $($b$)$ Determine the sum$-$of$-$products equation for F$.$ Show the terms instead of the minterm abbreviations $($show ABC instead of m$7).($c$)$ Determine the product$-$of$-$sums equation for F$.$ Show the terms instead of the maxterm abbreviations $($show A$\text{'}+$B$\text{'}+$C$\text{'}$ instead of M$7).($d$)$ Prove that F from question b is equivalent to F $=$ A$\text{'}+$ B$\text{'}$C$\text{'}$ using proof by rewrite. HINT: remember the uniting law is the key to minimization. $($e$)$ Draw the gate diagram for F$=$ A$\text{'}+$ B$\text{'}$C$\text{'}.$