Please solve properly with detailed explanation

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. 5. Assuming that (i) x(Q(x)S(x)) (ii) x(Q(x)P(x)) (iii) x(P(x)R(x)) prove or disprove that the hypotheses could lead to the conclusion: x(R(x)S(x)) Also, specify all inference rules used in the proof. (10 pts)