10 ) V (PAR) (Hint: First rewrite the conclusion.) 33. PV (QAR) (PVO) A (PVR) (Hint: Prove both PV(AR) - (PVO) and PVCOAR) - (PVR); for each proof, first rewrite the conclusion.) TABLE 1.14 From P-Q, Q-R PVQP PQ Q' P' IP PVP (PAQ) R P.P. PAQVR) PV (QAR) 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-( Q R) (Exercise 30] Exportation-exp Q [Exercise 31] Inconsistency-inc (PAQ) V (PAR) (Exercise 32] Distributive-dist (PVQ) A (PVR) (Exercise 33) Distributive-dist For Exercises 3442, 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. ( PQ)^(P' Q) 36. (A' B') A ( A C) ( BC) 37. (A' + B) ^ (B +C) A( C D ) (A' + D) 38. (A V B) A (A C) A (B +C) C 39. (YZ') A (X' YA [Y ( XW)]^(Y Z) (YW) 40. (A A B)^(B A')+(CAB') 41. (A A B)'A(C' 1A)'A(CA B')' A' 42. (PV (QAR)) ^ (R' V S) A (S T') ( T P) In Exercises 4354, write the argument using propositional wffs (use propositional logic, including the rules in Table 1.14, prove that the a