Quiz 2

Quantifier Manipulation

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# Quantifier Manipulation ## Swapping Quantifiers - $\forall x \exists y P(x,y)$ is NOT equivalent to $\exists y \forall x P(x,y)$ - $\forall x \forall y P(x,y) \equiv \forall y \forall x P(x,y)$ - $\exists x \exists y P(x,y) \equiv \exists y \exists x P(x,y)$ [Join Discord](https://discord.gg/gE2m4Qrdqv) [Previous*...

Quantifier Manipulation

Swapping Quantifiers

  • ∀x∃yP(x,y)\forall x \exists y P(x,y) is NOT equivalent to ∃y∀xP(x,y)\exists y \forall x P(x,y)
  • ∀x∀yP(x,y)≡∀y∀xP(x,y)\forall x \forall y P(x,y) \equiv \forall y \forall x P(x,y)
  • ∃x∃yP(x,y)≡∃y∃xP(x,y)\exists x \exists y P(x,y) \equiv \exists y \exists x P(x,y) Join Discord PreviousPredicate LogicNextProof Techniques
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