Let $P(x,y)$ be a propositional function.
Now, consider the following statements:
i. $\forall y \exists x P(x,y) \rightarrow \exists x \forall y P(x,y) $ is a tautology.
ii. $\forall x \exists y P(x,y) \rightarrow \exists x \forall y P(x,y) $ is a tautology.
(Assume domain of all quantifiers are same and it is non-empty)
Which one of the following statements is correct ?
- $(i)$ is correct but $(ii)$ is incorrect
- $(ii)$ is correct but $(i)$ is incorrect
- Both $(i)$ and $(ii)$ are correct
- None of them are correct
