52-54 discrete

In Exercises 43-54, write the argument using propositional wfls (use the statement letters sho propositional logic, including the rules in Table 1.14, prove that the argument is valid. 43. If the program is efficient, it executes quickly. Either the program is efficient, or it has a bug. How 44. If Jane is more popular, then she will be elected. If Jane is more popular, then Craig will resign. T 45. If chicken is on the menu, then don't order fish, but you should have either fish or salad. So, if chic 46. The crop is good, but there is not enough water. If there is a lot of rain or not a lot of sun, then ther 47. If the ad is successful, then the sales volume will go up. Either the ad is successful or the store 48. If DeWayne is not tall then Jayden is not DeWayne's brother. If DeWayne is tall then Trevor is De Way 49. Russia was a superior power, and either France was not strong or Napoleon made an error. Napoleon did 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 51. If Jose took the jewelry or Mrs. Krasov lied, then a crime was committed. Mr. Krasov was not in town. If 52. If the birds are flying south and the leaves are turning, then it must be fall. Fall brings cold weather. The 53. If a Democrat is elected then taxes will go up. Either a Democrat will be elected or the bill will pass 54. Either Emily was not home or if Pat did not leave the tomatoes, then Sophie was ill. Also, if Emily was not program does not execute quickly. Therefore, it has a bug. E, O. B if Jane is more popular, she will be elected and Craig will resign. J. E. C on the menu, have salad. C, F, S enough water. Therefore, the crop is good and there is a lot of sun. C. W, R. S The sales volume will not go up. Therefore, the store will close. A, S.C brother. Therefore, if Jayden is DeWayne's brother, then Trevor is De Wayne's brother. D not make an error, but if the army did not fail, then France was strong. Hence, the army failed and Russia was a superior power. R, F, N, A will be built or bills will not be late. Therefore, usage will not go down and bills will be late. R, U. P. B a crime was committed, then Mr. Krasov was in town. Therefore, Jose did not take the jewelry. J L. C.T leaves are turning but the weather is not cold. Therefore, the birds are not flying south. B, L. F. C Therefore, if taxes do not go up, then the bill will pass. D, T, B home, then Olivia left the peppers. But it is not true that either Sophie was ill or Olivia left the pepper Therefore, Pat left the tomatoes and Olivia did not leave the peppers. E. P, S, O