Please answer #40, it needs to be in a proof sequence format and my teacher said to use the inconsistency rule on table 1.14

Use propositional logic to prove that the argument is valid

(A ^ B) ^ (B -> A) -> (C ^ B)

TABLE 1.14 From PQ, QR PVQ, P. PQ Q-P More Inference Rules Can Derive Name/Abbreviation for Rule P-R [Example 16) Hypothetical syllogism-hs Q [Exercise 25] Disjunctive syllogism-ds Q' P' [Exercise 26] Contraposition-cont P Q [Exercise 27] Contraposition-cont PAP[Exercise 28] Self-reference-self P [Exercise 29] Self-reference-self P ( QR) [Exercise 30] Exportation-exp Q [Exercise 31] Inconsistency-inc (PAQ) V (PAR) [Exercise 32] Distributive-dist (PVQ) (PVR) (Exercise 33] Distributive-dist PVP (PAQ R PP PAQVR) PVQAR) For Exercises 34-42, use propositional logic to prove the arguments valid; you may use any of the rules in Table 1.14 or any previously proved exercise. 34. A' (A + B) 35. (P A(P' Q) Q 36. (A' B') ^ (A C)(BC) 37. (A'B)^( BC)^(C+D) (A' D) 38. (A V B)^(A C) A (B+C)C 39.(Y Z') ^ (X Y)A[Y ( XW)]^(YZ 40. (A AB) A (B A') (CA B') 41. (A A B)' ^ (C' 1A)' AC A B')' A' 42. (PV (QAR)) A (R' VS) A ( ST") ( TP) In Exercises 4354, write the argument using propositi nronositional logic including the rules in Table 1.14, p