Using this glossary:
$Gx: x \text{ is green}$
$Hx: x \text{ is heavy}$
$Rx: x \text{ is red}$
My textbook says that the sentence "All red things heavy, but some green things aren't" is translated to: $$\forall{x} (Rx \implies Hx) \land \exists{x} (Gx \land \lnot{Hx})$$
But on the doing the exercise I couldn't figure out why it was translated this way. Isn't it more obvious to translate it this way?
$$\forall{x} (Rx \implies Hx) \land \exists{x} (Gx \implies \lnot{Hx})$$
I would like to know why the former is correct and the latter is wrong.
$\exists x (Gx \implies \neg Hx)$ can be translated to: there is some thing, where if it is green, it is not heavy.
This does not assert the existence of anything green. If there is some red object (heavy or not), this statement is vacuously true.
Whereas $\exists x (Gx \land \neg Hx)$ can be translated to: there is some thing which is green and not heavy.
This asserts the existence of a green object that is not heavy.