S and T are binary relations on the set $\{$a$,$ b$,$ c$,$ d$\}$ and are defined as follows: S $=\{($a$,$ b$),($a$,$ c$),($b$,$ d$),($d$,$ c$)\}$

T $=\{($b$,$ b$),($c$,$ a$),($c$,$ d$),($a$,$ d$)\}$

Select the set corresponding to

$.$