Question $3[$Propositional Logic$]$

Let $F$ be the formula $(AvvnotB)BA,$ and let $G$ be the formula $(AB)$notB$$not$(AvvB).($See the logic cheat sheet below for the Natural Deduction rules for Propositional Logic.$)$

$($a$)$ Provide parse trees corresponding to $F$ and $G.$

$[4$ marks$]$

$($b$)$ Provide a constructive Natural Deduction proof of $F.$

$[6$ marks$]$

$($c$)$ Provide a constructive Natural Deduction proof of $G.$

$[6$ marks$]$

$($d$)$ Is $F$ satisfiable? Is $G$ valid? Justify your answers.

$[4$ marks$]$