natural language example to show difference between first order logic propositions

Question

while discussing some problem in formal logic i came across two different formulas: $ \lnot \exists y (P(y) \land Q)$ and $ (\lnot \exists y P(y))\land Q$

now, these 2 are obviously not equivalent, as the first one is trivially true when Q is false, while the second one is false when Q is false.

i tried to think of an example in natural language that highlights their difference, but could not come up with one.

any ideas how to express these 2 different concepts in ordinary language?

Answer 1

Here's a contrivance:

1. $ \lnot \exists y \:(P(y) \land Q)$

   There is no deer that is herbivorous, which is to say, animal-eating. (TRUE)

      (The given property is is incoherent as it contradicts an accepted definition.)

2. $ \lnot \exists y P(y)\land Q$

   There is no deer that is herbivorous, and herbivorous means animal-eating. (FALSE)

      (The second conjunct is analytically false.)