please help me with question 34, 36 and 38. Thank you

34. Give interpretations to prove that each of the following wffs is not valid: a. (Ex)A(x) ^ (3x)B(x) (Ex)[A(x) A B(x)] b. (Vx)Ey)P(x, y) (Ex)(Vy)P(x, y) c. (Wx)[P(x) Q(x)] [(3x)P(x) (Vx)Q(x)] d. (Vx)[A(x)]' + [(Vx)A(x)]' 35. Decide whether each of the following wffs is valid or invalid. Justify your answer. a. (3x)A(x) ((Vx)[A(x)]')' b. (Vx)P(x) V (Ex)Q(x) (Vx)[P(x) V Q(x)] 36. Decide whether each of the following wffs is valid or invalid. Justify your answer. a. (Vx)A(x) (Ex)[A(x)]')' b. (Vx)[P(x) Q(x)] ^ (Ex)[P(x) V Q(x)] (3x)[P(x) ^ Q(x)] c. (Vx)[P(x) V Q(x)] (Vx)P(x) V Ey)2(y) 37. From Example 24c, we know that (Vx)[P(x) ^ Q(x)] + (Vx)P(x) ^ (Vx)Q(x) is valid. From Prac- tice 21, we know that (Vx)[P(x) V Q(x)] + (Vx)P(x) V (Vx)Q(x) is not valid. From Exercise 34a, we know that (3x)[P(x) ^ Q(x)] H (3x)P(x) ^ (3x)Q(x) is not valid. Explain why (Ex)[P(x) V Q(x)] + (3x)P(x) V (Ex)Q(x) is valid. 38. A predicate wff is in prenex normal form if all the quantifiers appear at the front of the wff. Write each of the following expressions as an equivalent wff in prenex normal form. a. (Vx)P(x) A (Vy)Q(y) b. (Vx)(P(x) (Vy)[Q(y) W(x, y)]) c. (3x)P(x) A (Ex)Q(x)