Having trouble with these questions from a recent practical and would really appreciate a detailed explanation on these question $($they$\text{'}$re made to be put into Carnap$)$

Derive a natural deduction proof in Carnap for each of the following arguments.

$($i$)$

$($P $$Q$)->$ R$,$R $$P $$ Q

$($ii$)$

P $$ Q$,$ Q $->$ R$,$ P $->$R $$P $$Q

$($iii$)$

$$x$($P $($x$)->$ Q$($x$)),$x$$Q$($x$)$x$($Q$($x$)$P $($x$))$

For each of the following $$Knights and Knaves$$ puzzles, formalise the sequence of statements using propositional logic and prove a proposition that demonstrates the nature of each individual in Carnap.

$($i$)$

Alice: $$We are both knights$.$ Bob: $$Alice is a liar!$$

$($ii$)$

Dan: $$It$$s fale that Ed is a knave$.$ Ed: $$I and Dan have a different nature.$$

$($iii$)$

Rex: $$Sally is a knave$.$ Joe: $$It$$s not the case that Rex is a knave$.$ Sally: $$Neither I nor Rex are knaves.$$