PHL 107
John Halpin
MOCK EXAM ONE

Do each of the following.

1. First, circle the conclusion indicator of the following argument, then put it in standard form. (On the real exam you may be asked to say whether or not the argument is VALID. But this one's a little hard to tell!) (3 pts.)

Because the world contains evil, and since God is supposed to be an all powerful and completely good creator of the world, it follows that such a God does not exist.

2. Which of the following are sentences of SL? Circle main connectives of those which are. You are allowed to drop outside parentheses or use brackets in place of parentheses. (6 pts.)

a) F~&~C

b) [F&(CD)]v~(DvL)

c) F&(T&(J&S))

d) (Av~B)=(Dv~B)v(L&~B)

3. Symbolize each of the following using A: Art is a student, B: Bill is a student, and C: Carol is a student. (4 pts.)

a) Bill is a student if Art is not.

b) Bill is a student unless Art is not.

c) Carol is a student only if Bob is.

d) Bob and Carol aren't both students.

4. For each of the following, say whether it is true or false, then fully explain your answer with an informal proof.

If you need to show that something holds in all cases, show this from the definitions:

Example i) All sound arguments are valid.

True Suppose that A is any sound argument. Then because being valid is one part of the definition of sound, A is valid.

Example ii) A logical truth can be false.

False We can show that all logical truths are NOT false. Suppose that S is a logical truth. Then because the definition of a logical truth states that it can't be false; S is not false.

If you need to show that something holds in at least one case, then give an example of such a case.

Example iii) All valid arguments are sound.

False because there are "counter" examples like "All dogs do calculus well, therefore all dogs can do calculus." This is valid but not sound.

Example iv) A logically indeterminate sentence can be true.

True because of examples like: "Halpin teaches logic"; this is logically indeterminate because it might have been false (I might have been a pilot instead of a professor), so it is neither logically true nor logically false.

(6 pts.)

a) No logically indeterminate sentence is false.

b) Any sound argument has a true conclusion.

c) All connectives of SL are truth functional.

(Answers)