Question $7.(8$ Marks$)$ Let P and Q be predicates on the set S$,$ where S has two elements, say, S$=\{$a$,$ b$\}.$ Then the statement $$ x P$($x$)$ can also be written in full detail as P$($a$)$ P$($b$).$ Rewrite each of the statements below in a similar fashion, using P$,$ Q$,$ and logical operators, but without quantifiers. $($a$)$ x$,$ y$($P$($x$)$ Q$($y$))($b$)$ x $$ y$($P$($x$)$ Q$($y$))($c$)$ x P$($x$)$ y Q$($y$)($d$)$ x $$ y$($P$($x$)$ Q$($y$))$