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Let A be any set. We define B such as:
$B = \{x \in A : x \notin x\}$

Can it be that $B \in A$? No.

Assume $B \in A$.

• If $B \in B$ then by the definition of B:
$B \notin B$. Contradiction.
• If $B \notin B$ then by the definition of B:
$B \in A \text{ and } B \notin B \implies B \in B$. Contradiction.

Therefore $B \notin A$.