Practice Exam #2

 

General Instructions: This quiz has five parts. Be sure to complete each part. Read the instructions completely before attempting to answer specific questions. Number your answers in your blue book, show all work and state the result., You may take up to the full class period to complete this exam.

 

Part I  True or False? (2 point each, 10 total)

 

1. If an argument in PL is valid, then there is a derivation whose premises are the premises of the argument and whose last line is the conclusion of the argument.

 

2. The wff ~(x)Fx is logically equivalent to (x)~Fx.

 

3. From two contradictory wffs in a derivation, anything follows.

 

4. If all the paths of a truth-tree are open, the wffs at the root (top) of the tree are all tautologies.

 

5. A sufficient condition for an argument being valid is that its premises contain a contradiction. 

 

Part II Proofs: Construct proofs of one of the following arguments. You may use conditional and indirect proof as needed. (20 points)

 

1.                (A ≡ B)  ⊃ C, ~(C v A), /// B

 

2.                (A & B) v (C & ~D), A ⊃ ~B, C ⊃ (D v F), /// F

 

3.                X ≡ ~Y, (Y v Z) ⊃ T, ~(T v W), /// P ⊃ X

 

Part III Proofs: Prove the one of the following theorems. (20 points)

 

1.               ~(~(P v Q) v P) ⊃ Q

 

2.               ~(~P & ~Q) ≡ (P v Q)

 

3.               (~P v Q) ⊃ (P ⊃ Q)

 

Part IV Answer one question (15 points)

 

1.     Explain the following:  PL is consistent. How could we change the proof theory of PL to make it inconsistent?

 

2.     Is there a decision procedure for determining whether there is a proof of some wff from some given premises? Explain.

 

Part V Translate the following argument into PL. (15 points)

 

1.     Oxygen isn't a sufficient condition for fire. Fire is a sufficient condition for chaos. Therefore Oxygen is a necessary condition for chaos.

 

Part VI  For each of the following sentences, determine whether it is a singular proposition. (2 points each, 10 points total)

 

1. All apples are green.

 

2. Fred is hungry.

 

3. Portland is a nice city.

 

4. Some mathematicians ride bicycles.

 

5. Everyone lives in New York.

 

Part VII Translate into QL. Be sure to provide a dictionary. Choose two. (5 points each)

 

1.  Ignat is tall but Bethsheba isn't.

 

2. Neither Arthur nor Dorothy  climb trees.
 

3. No one is happy.
 

4. Someone isn't home.
 

5. Not all are here.