Problem $3.$ For this problem, note that logic circuits can use the same variable multiple times as input to $1\mathrm{.}2$ Applications of Propositional Logic

FIGURE $3$ The circuit for $(pvvnotr{)}^{{?}^{?}}(notpvv(qvvnotr))$multiple basic gates. As an example, see Figure $3$ on page $23$ of your textbook.

$($a$)$ Draw a logic circuit that produces the output $(($p $$r$)$q$)($p $($q $$ r$))$ from inputs p$,$ q$,$ r$.$

$[2$ points$]$

$($b$)$ Draw the simplest possible logic circuit that produces the output $($p $$ q$)$p $$ q$.$