Using only the 12 basic intro/elim rules of Natural Deduction (you may not use logical equivalences), prove the following: Solution: Using only the 12 basic intro/elim rules of Natural Deduction (you may not use logical equivalences), prove the following: Solution: (pq) ^ (pr) ..p (q^r) Vx(P(x) Q(x)) Vx(Q(x) R(x)) .. Vx(P(x) R(x)) Using only the 12 basic intro/elim rules of Natural Deduction (you may not use logical equivalences), prove the following: Solution: Vxy[P(x, y) ^ Q(y)] Vxyz[P(x, y) ^ Q(y) ^ Q(z)] Note: We assume that all variables are in the same domain.