Axiomatic Set Theory & Intro to Topology – Lecture 2 (Topology)

Axiom 1 says "X ∈ Y is a proposition if and only if X and Y are sets." How does this defeat the "set of all sets that don't contain themselves" paradox?

1. A.It proves the paradoxical collection exists but turns out to be the empty set
2. B.It blocks the construction: the membership condition isn't a proposition
3. C.It shows the set both contains and does not contain itself, and treats that as allowed
4. D.It restricts membership to sets of finite cardinality, excluding the construction