pls only use the laws on natural desuction to solve... (you cannot use logical equivalencies)

a) Using only the 16 basic intro/elim rules of Natural Deduction (you may not use logical equivalences), prove that Vr (S(r) A C(r)] .. Vx (S(x) + C(x)] b) But wait! In Lecture 3 (slides 39-41) we said that Vr (S(r) AC(r)] #V: [$(x) + C(x)] Show why the converse of (a) does not hold. In particular, use a counterexample to show that it is NOT the case that Vx ($(x) + C) Vx (S(2) AC()]