Use propositional logic to prove the validity of the arguments in Exercises 25-33. These will become additional derivation rules for propositional logic, summarized in Table 1.14 PAQVR) (PAQ) (PAR) hint: First rewrite the conclusion Do not use distributive rule directly. This question is to prove the "distributive rule" TABLE 1.14 From PQ, QR PVQ,P PQ QP More Inference Rules Can Derive Name/Abbreviation for Rule PR [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) A (PVR) [Exercise 33] Distributive-dist PVP (PAQ R P.P PAQ VR) PV (QAR)