Q Homework Translation II (Translating Arguments) Examples: (See the video short from this week to see the solutions to 1 through 3 below.) #1: (P1) The Giants won the World Series in 2010 and 2012. (P2) If the Giants won the World Series in 2010 and 2012, there would be two parades in SF. Therefore, (P3) There would be two parades in SF. #2: (P1) It is not the case that Mitt Romney won the election. (P2) If Mitt Romney won the election, the Republicans would have been happy. Therefore, (C) The Republicans were not happy. #3: (P1) Plato wrote The Republic and Aristotle wrote The Nicomachean Ethics. (P2) The Republic is a classic work in philosophy. Therefore, (P3) Plato wrote a classic work in philosophy. Exercise 1: Translate the following arguments into propositional logic. Example: (P1) If John is happy, he will dance. (P1) J ? D (P2) John is happy. (P2) J Therefore, Therefore, (C) John will dance (C) D #1: (P1) If I pass my chemistry class, I will graduate. (P2) If I do not pass my chemistry class, I will not graduate. Therefore, (C) I should study for my chemistry exams. #2: (P1) If you eat well and exercise, you will have good health. (P2) You have good health. Therefore, (C) You eat well and exercise. #3: (P1) I will have a sandwich or a burrito for lunch. (P2) If I have a sandwich, I will exercise in the afternoon. (P3) If I have a burrito, I will not exercise in the afternoon. Therefore, (C) I will exercise in the afternoon. #4: (P1) The Warriors will win only if Kevin Durant scores more than 30 points. (P2) If Kevin Durant scores more than 30 points and Stephen Curry plays good defense, the Warriors will win. (P3) Kevin Durant will score more than 30 points. (P4) Stephen Curry will play good defense. Therefore, (C) The Warriors will win. #5: (P1) Either the butler committed the murder or the ex-husband committed the murder. (P2) The ex-husband was out of town at the time of the murder. (P3) If the ex-husband was out of town, he did not commit the murder. Therefore, (C) The butler committed the murder. #6: (P1) Either you pass the class or not pass the class, but not both. (P2) If you do not study for your exams, you will not pass the class. (P3) If you study for your exams, you will pass the class. (P4) You studied for your exams. Therefore, (C) You passed the class. #7: (P1) Simon is sane or deluded, but not both. (P2) Simon believes both that the moon is made of green cheese and that it is not made of green cheese. (P3) If Simon believes both that the moon is made of green cheese and that it is not made of green cheese, he is deluded. Therefore, (C) Simon is deluded.

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