No one is perfect. $$x$($p$($x$))$

Not everyone is perfect. $($p$($x$))$

All your friends are perfect. $$x$($q$($x$)->$p$($x$))$

At least one of your friends is perfect. $$x$($q$($x$)->$p$($x$))$

Everyone is your friend and is perfect. $$x$($q$($x$)$p$($x$))$

Not everybody is your friend or someone is not perfect.$$x$($q$($x$)($x$$p$($x$)))$