I am a student of logic who just became familiar with first-order predicate logic. I got stuck in this problem. Although I was hinted to translate→into ¬,∨ to solve the problem, I still have no idea what to do next. Here is the problem:
Use semantics under the substitution to check whether 1> ∃x (Pa→Qx) ⇔Pa →∃x(Qx)
2> ∃x (Px→Qa) ⇔∃x(Px) →Qa. If either 1> or 2> fails, can you suggest a rectification?