Suppose that S$0,$ S$1,$ S$2,...$ is a sequence of subsets of N$.$ Which one of the following sets is guaranteed to be different from all sets in the sequence?

$($a$)$ S$=\{$n$|$n$$ in Sn$2\}($b$)$ S$=\{$n$|$n$2$ in Sn$2\}($c$)$ S$=\{$n$2|$n$$ in Sn$2\}($d$)$ S$=\{$n$2|$n$2$ in Sn$\}$

$($e$)$ S $=\{$n$2|$ n $$ in Sn$\}$

Explain why your chosen set is guaranteed not to be in the sequence S$0,$ S$1,$ S$2,...$