Show that the following $($formalized$)$ arguments are valid by deriving conclusions from the given premises by utilizing inference rules.

$\{5\}[11]$ C: A

$-------------------------------------------------$

P$1$: ~B

P$2$: $($C $$ ~D$)($A $$ ~D$)$

P$3$: D $$ B

P$4$: B $$ C

$-------------------------------------------------$

$\{5\}[12]$ C: ~Y $$ ~X

$------------------------------------------$

$1.($Q $$ U$)$ Y

$2.$ X $($Q $$ T$)$

$------------------------------------------$

$\{5\}[13]$ C: ~Q

$-------------------------------------------$

$1.$ R $$ S

$2.$ Q $($S $$ T$)$

$3.$ ~R $$ ~S

$-------------------------------------------($Hint: Use IP$)$

$\{5\}[14]$ C: A $$ B

$--------------------------------------------$

$1$: A $$ ~C

$2$: ~B $$ C

$3$: A $$ ~B

$--------------------------------------------($Hint: Use CP twice$)$