Construct natural deduction proofs demonstrating the following. Besure to handwrite your solutions, and properly annotate your proof to show your working.

$($a$)(($C $->$ E$)($C $->$E$))$ C $$ E;

$($b$)((($A $$ B$)->$ C$)(($A $$ B$)->$ C$))($B $->$ C$)$;

$($c$)((($Q $->$P$)($Q $$R$))->($P $->$ R$)).$