Philosophy 251: Handout #4

VI. Translate each of the following sentences into formulas of SL.

1. If Bob jogs regularly, then he is not lazy.
2. David jogs regularly unless he works too much.
3. Carol jogs regularly if and only if she protects the president.
4. Carol protects the president only if she is a Secret Service agent.
5. Bob protects the president except when he is abroad.
6. If Carol jogs regularly, then if Bob is not lazy he jogs regularly.
7. If both David and Carol protect the president, then Al does too.
8. Provided neither Carol nor Bob protect the president, then Al doesn't either.
9. Assuming Carol is not protecting the president, Bob does if and only if both Al and David don't.
10. Albert does not jog regularly only if he works overtime, unless he is protecting the president.
11. If Carol jogs regularly and Bob is not lazy and Al is not working overtime, they all protect the president.
12. If Al works overtime only if Carol does, then Al and Carol protect the president exactly when Bob does.
13. If Al protects the president if he jogs regularly, then if Bob is lazy he doesn't jog regularly.
14. Bob protects the president except when Al does not, unless Carol or David or Al is not an agent.
15. If Al is an assassin and not a Secret Service agent, then Carol and Bob are in trouble unless David saves the president.

VII. Translate each of the following sentences into formulas of SL.

1. In order to ace intro logic, it is sufficient that you get a hundred on every exam.
2. In order to pass, it is necessary that you average at least fifty.
3. Receiving a degree and doing an internship are necessary for becoming a physician.
4. Taking all the exams is necessary, but not sufficient for acing intro logic.
5. In order to get into medical school, it is necessary but not sufficient that you have good grades and take the admissions exam.
6. Committing a crime and getting caught are sufficient, but not necessary for getting arrested.
7. If it is raining, I will play basketball; otherwise, I will go jogging.
8. If George and Elliot are home this weekend, we will go to the theatre; otherwise, we will stay home.
9. Alice will win the championship unless she gets injured, in which case John will win.
10. If you make an appointment and do not keep it, then I shall be angry unless you have a good excuse.
11. Provided that you are intelligent, you will fail if and only if you goof off.
12. I am happy only if my assistants are competent, but if my assistants are competent, then they get transferred to better jobs and I am not happy.
13. If you do not concentrate well unless you are alert, then provided you are not a maniac you will fly an airplane only if you are sober.
14. Provided that your concentrating well is a necessary condition for your passing, if you concentrate well only if you are threatened, then you will not pass unless you are threatened.
15. If neither Alex nor George is home this weekend, we will either go to the beach or see a movie; otherwise, we will go camping unless it rains, in which case we will stay home.