Determine whether the following pairs of logical statements are equivalent.

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

$($b$)($p $->$ q$)->($r $->$ s$)$ and $($p $->$ r$)->($q $->$ s$)$

$($c$)$x$($P$($x$)$ Q$($x$))$ and $$xP$($x$)$xQ$($x$)$

$($d$)$x $($P$($x$)$ Q$($x$))$ and $($x $($P$($x$)$Q$($x$)))$