Part $3($#$912)$: Use the first $13$ rules of inference $($the $8$ rules of implication and first $5$ rules of replacement$)$ to provide logical proofs with line$-$by$-$line justifications for the following arguments.

The logical operators used must be the ones we are using in this class; no other operators will be accepted. The method used to solve each problem must be the method we are using in this class; no other methods or steps will be accepted.

$9.$

$1.$ ~$($A & B$)/$~B v ~A