Decide whether the given arguments in exereises 42 -48 are valid or invalid. Draw the Venn diagram for questions 42, 43, 45. 46, 47, 48.

42. 43. 44. 45. 46. 47. 49. 50. Some teachers are absent-minded. Mrs. Milne is a teacher. Mrs. Milne is absent-udnded. All frogs are green. Kermit is a frog. Kermit is green. If I do not study, I'll get a bad grade. I study I'll get a good grade. All vehicle-owners have a mechanic. Kyle has a mechanic. Kyle owns a vehicle. All birds y. All planes z. A bird is not a plane. All zigs are zags. All zags are 028. All zigs are zoops. All kicks are wicks. Some wicks are knicks. Some kicks are knicks. Translate the following into symbolic notation and prove that \"I play golf and I go skiing" is the valid conclusion. If I don't play golf (p) or i don't go skiing (s). then I have had a rotten year (r). If I have had a rotten your. then I'm grumpy (g) or! make up hard exams (h). I'm not grumpy and I'm not old (0). If I'm not old, then I do not make hard exams. Every statement made by a fortune-teller on Monday through Friday is false. Every statement she makes an a weekend is true. a) On which days of the week can she make the statement, \"I lied yesterday"? b) On which days of the week can she make the statement. \"I will be lying tomorrow\"? 1-54 c) On which days of the week can she make the statement. \"I lied yesterday and I will be lying tomorrow&quot