Please solve correctly with proper reasoning

3. 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 4. Prove the following claims using direct proof. Before beginning your proof, state the assumptions given, and state the conclusion you must prove. (20 pts) (a) For any set of three integers x,y,z, if x divides y and y divides z, then x divides z. (b) For any pair of integers x,y, if x and y are odd, then xy is odd