I have to give a counterexample for the following argument schema:
∃x (Px ∧ Qx) ⊨ ∀x (Px ∨ Qx)
by definig its domain and the interpretation function, which is where I have some slight problems. On a technical level, I think I understood, what's the problem with the schema, namely, that the conclusion is false because of the universal quantifier.
But I don't really understand how to express this in an interpretational function, that proves that the first statement is true, where as the second is false.