Find a model to demonstrate that the following sequent is no

Find a model to demonstrate that the following sequent is not valid: ((exist x) F(x)) ((exist y) G(y)) (Forall x) (~ G(x) ~ F(x)) Briefly justify your answer.

Solution

Let F(x) = There is a girl in school bus of school A

G(x) = girls do study in school A

If there is a girl in school bus then there are girls studying in school A

But if there is no girl in school bus it does not implies that no girl studies in school A. They might be using some other means of transportation.