Find an error in the following proof and explain why it is an error. (a) Proving P(x)xP(x) (1) P(x) - premise (2) xP(x) - universal generalization (b) Proving xP(x)yP(y) (1) xP(x) - premise (2) P(y) - existential instantiation ( y in a new free variable name) (3) yP(y) - universal generalization (c) Proving x(P(x)Q(x)),x(P(x)R(x))x(R(x)Q(x)) (1) x(P(x)Q(x)) - premise (2) P(c)Q(c) - universal instantiation (c is a constant) (3) x(P(x)R(x)) - premise (4) P(c)R(c) - existential instantiation (5) P(c) - conjunction elimination (6) Q(c) - modus ponens for (2) and (5) (7) R(c) - conjunction elimination for (4) (8) R(c)Q(c) - conjunction introduction for (6) and (7) (9) x(R(x)Q(x)) - existential generalization