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1 Answer

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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

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