NOTE: The format of the real first midterm will follow this format exactly. However, since I cannot duplicate our normal symbols for conjunction (dot), conditional (horseshoe) or biconditional (triple-bar) in HTML, I have used the following substitutions: conditional ->, biconditional <->, and conjunction &. The real exam will, however, use the normal symbols.

Midterm I

Philosophy 500 -- Introduction to Logic

Write your name here: ______________________________

The exam consists of 20 questions. Each is worth 5 points. Show all work.

Part One. Give a one sentence definition of the following terms.

1. Argument

2. Justified Step

3. Logically Equivalent

4. Tautology

5. Statement form

Part Two. Short answer.

6. Explain the difference between a statement and statement variable.

7. Explain the difference between a valid argument and a sound argument.

Part Three. Truth tables.

In 9 and 10, use truth tables to determine if the given statement has a form that is contingent, a contradiction, or a tautology. You will first need to translate from the English to proper logical symbolism.

9. If I don't bowl a 300 game, then if I don't bowl a 300 game, I will go to the Bowling Hall of Fame.

10. If both either my ex-fiancee is cheap or she has no scruples and I got hosed then either my ex-fiancee is cheap or she has no scuples or I got hosed.

In 11 and 12, use truth tables to determine if the following argument forms are valid. You may use a partial truth table if you like. Explain your reasoning.

11.

p -> q
~p

Therefore: ~q

12.

p -> q
~q -> r

Therefore: ~p v r

In 13 and 14, use truth tables to determine if the given statement forms are consistent, equivalent, and if either logically entails the other. Explain your answer briefly.

13. p -> ~q , ~p v q

14. p & ~r , (q -> ~p) v r

Part Four. Proofs.

Construct proofs for the following arguments. In 15 and 16 you may use all rules of inference and all replacement rules, but not conditional or indirect proof. In 17 and 18 you may also use conditional and indirect proof. In 19 and 20 you MUST use either condiitonal or indirect proof, or both. You must justify every step.

15.

1. (A v B) -> ~C
2. C v D
3. A \ D

16.

1. [(J -> J)] & K
2. J v ~J
3. ~K \ ~(J & ~J)

17.

1. B & D
2. (G -> B) -> (B -> C)
3. (B -> C) -> (D -> E)
4. B -> (G -> B) \ E v G

18.

1. H <-> J
2. ~H \ ~J

19.

1. (P & S) -> (T v W)
2. ~T <-> ~(M & O)
3. ~(W v (~S v M))
4. ~A -> P \ A

20.

1. A -> C \ (A & B) -> C