In Exercises 4354, 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.

50. . 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

52.. If the birds are flying south and the leaves are turning, then it must be fall. Fall brings cold weather. The leaves are turning but the weather is not cold. Therefore, the birds are not flying south. B, L, F, C