First order logic. Describing that there exists a set with exactly 2 elements

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∃∃(∈ ∧ ∈ ∧ ¬(=))

Is this a valid way to describe that? I believe it's correct but I'm not so sure

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$\exists A \exists x \exists y ~(x \in A \land y \in A \land \lnot (x=y) \land \forall z (z \in A \Rightarrow (z=x \lor z=y)))$.