Question

Predicate Logic/Calculus

Answer 1

I'm trying to find a model (universe, definition of predicates) where the following is satisfiable but not true.

\[\exists y A(x,y) \rightarrow \forall x \exists y A(x,y)\]

I know that the free variable x occurs in the first part of the implication. To show that it is not true for all x, I simply quantify x with the universal quantifer and to show it is satisfiable, I quantify x with the existential quantifier. I'm having trouble beyond those steps.

Answer 2

*