$\exists(X)$ $\bullet$ $\forall$(Y) $\bullet$ p(X) $\Rightarrow$ p(Y)
I am struggling to give to a structure for the following formula, one such that the truth value of the formula is T and one such that is it F.
I am reading the formula as follows
There exists some X that implies all Y
and that the predicate is the same..so p could be isBlue for example
There is exists some X which is blue that implies all Y is blue
More correctly: "There is something which, if it is blue, then everything is blue."
The existential statement does not guarantee that it has a witness that is blue. Only that everything will be blue if that witness is.
I remind you of two facts:
(1) Implications are valued true when the consequent is true or the antecedent is false.
(2) Existential statements are vacuously false for empty domains.
This will give you three structures to examine.