Answer : C
$S_1$ : Russel's Paradox shows that $S_1$ i.e. "set of all sets that do not contain themselves," does not exist.
Set $S_1$ is a Set of All the Sets which do not contain themselves as element. This is known as "Russel's Paradox".
Russell's paradox is a counterexample to naive set theory, which defines a set as any definable collection. The paradox defines the set of all sets that are not members of themselves, and notes that
- if $R$ contains itself, then $R$ must be a set that is not a member of itself by the definition of $R$, which is contradictory;
- if $R$ does not contain itself, then $R$ is one of the sets that is not a member of itself, and is thus contained in $R$ by definition--also a contradiction.
$S_2$ : Cantor's paradox --- shows that "the set of all sets" cannot exist.
https://en.wikipedia.org/wiki/Cantor%27s_paradox