Let F(x,y,t) mean Person x can fool person y at time t.
Now $ \forall x \exists y \exists t (\neg F(x,y,t)) $ means ?
I can write it as
$ \neg \exists x \forall y \forall t (F(x,y,t)) $
I am having doubt of how to interpret the negation outside. Does it apply only to x ?
Should the predicate be " There does not exist x who can fool everyone all the time " or " There does not exist x who can fool someone at some time" ?
In first interpretation, I am applying negation to only x (not exists). Is it allowed ?