Show that the following arguments are valid using inference rules:

$($a$)$ p $-$q$,$ p $->($r $$ s $$ t$),-$s$,-$t $$ q

$($b$)($p $$ q$)->$ r$,(-$q $-$t$)->$ s$,(-$s $$ u$),$ p $(-$u $$ t$)$ r

$($c$)-$q $->$ p$,$ q $->($s $$ t$),$ u $->-$s$,$ u$,-$t $$ p

$($d$)(-$p $-$q$)->($r $$ s$),$ r $->$ w$,-$w $$ p