Write the argument using propositional wffs (use the statement letters shown). Then, using propositional logic, including the rules in Table 1.14, prove that the argument is valid. It is not the case that if electric rates go up, then usage will go down, nor is it true that either new power plants will be built or bills will not be late. Therefore, usage will not go down and bills will be late, R, U, P, B TABLE 1.14 From P Q Q R PVQ, P' PQ Q P 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 (P VQ) A (PVR) (Exercise 33) Distributive-dist P PVP (PAQ) R PP PAQVR) PV (QAR) Write the argument using propositional wffs (use the statement letters shown). Then, using propositional logic, including the rules in Table 1.14, prove that the argument is valid. It is not the case that if electric rates go up, then usage will go down, nor is it true that either new power plants will be built or bills will not be late. Therefore, usage will not go down and bills will be late, R, U, P, B TABLE 1.14 From P Q Q R PVQ, P' PQ Q P 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 (P VQ) A (PVR) (Exercise 33) Distributive-dist P PVP (PAQ) R PP PAQVR) PV (QAR)