Which statement about the function f$($x$)=$x$+2$from the set of real numbers to the set of integers is correct?

$($a$)\{\{2\}\}$P$($S$)$; $($b$)\{1,3\}$P$($S$)$; $($c$)\{1,3\}$ in P$($S$)$; $($d$)\{\{2\},\{4\}\}$P$($S$)$; $($e$)\{4\}$P$($S$).$

Which of these five statements are true?