The quantification $\exists ! x P(x)$ denotes the proposition “There exists a unique x such that P(x) is true”, express he quantification using universal and existential quantifications and logical operators?
- $\exists x P(x) \vee \forall x \forall y ((P(x) \vee P(y)) \rightarrow x=y)$
- $\forall x P(x) \wedge \forall x \forall y ((P(x) \vee P(y)) \rightarrow x=y)$
- $\exists x P(x) \wedge \forall x \forall y ((P(x) \wedge P(y)) \rightarrow x=y)$
- $\exists x P(x) \wedge \forall x \forall y ((P(x) \vee P(y)) \rightarrow x=y)$