Use De Morgan$$s law for quantified statements and the laws of propositional logic to show the following equivalences:

$($a$)$x $($P$($x$)$Q$($x$))$x $($P$($x$)$ Q$($x$))$

$($b$)$x $($P$($x$)->$ Q$($x$))$x $($P$($x$)$Q$($x$))$

$($c$)$x $($P$($x$)$ v $($Q$($x$)$R$($x$)))$x $($P$($x$)($Q$($x$)$ v R$($x$)))$