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$))$