Translating a sentence into symbolic form.

Question

If G(x) = "x is green" and the sentence is "Some animals are green and some are not green."

Then is my symbolic sentence correct? $$\exists x G(x) \land \exists y \lnot G(y)$$

Answer 1

Yes. $$\exists x G(x) \land \exists y \lnot G(y)$$ is correct, provided $x, y$ belong to the domain of all animals.

You might also want to add a predicate $$A(x):\;\;\text{"x is an animal"}$$ where the domain of $x$ (or $y$) is all things.

Then you'd have $$\exists x [A(x) \land G(x)] \land \exists y[A(y) \land \lnot G(y)]$$