Let $S=\{a,b,c\}.$ Mark each of the following statements as true or false.

$($a$)\frac{O}{i}nP(S)$

$($b$)\frac{O}{s}$ubeP$(S)$

$($c$)\{a\}inS$

$($d$)\{a\}inP(S)$

$($e$)$ ainS

$($f$)$ ainP$(S)$

$($g$)\{a\}subeS$

$($h$)\{a\}subeP(S)$

$($i$)$ asubeS

$($j$)$ asubeP$(S)$