Let the predicates $D(x,y)$ mean “team $x$ defeated team $y$” and $P(x,y)$ mean “team $x$ has played team $y$”. The quantified formula for the statement that there is a team that has beaten every team it has played is:
- $\exists x \forall y (P(x,y) \rightarrow D(x,y))$
- $ \forall x \exists y (P(x,y) \rightarrow D(x,y))$
- $ \forall y \exists x (P(x,y) \rightarrow D(x,y))$
- $\exists x \forall y (D(x,y) \rightarrow P(x,y))$