Prove the following propositional logic sequents using natural deduction. You are NOT allowed to use the derived rules.

$($a$)$ p$->($q$$r$)($p$->$q$)($p$->$r$)$

$($b$)$ r$->($p$->$q$),$p$$r$->($p$$q$)$

$($c$)$ p$->$q$(($p$$q$)->$p$)($p$->($p$$q$))$

$($d$)($q$$p$)$q$$p