In Problems $1$ and $2$: $$ If the formula is universally valid, provide a proof demonstrating its universal validity. $$ If the formula is not universally valid, construct and present a valuation under which the formula evaluates to $0($false$).$ Problem $1$: $[10$ marks$]($x$(($P$($x$)$ Q$($x$))($Q$($x$)$ P$($x$))))(($xP$($x$))($xQ$($x$)))$ Problem $2$: $[10$ marks$](($xP$($x$))($xQ$($x$)))($x$(($P$($x$)$ Q$($x$))($Q$($x$)$ P$($x$))))$