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Philosophy 117OL: Traditional Logic EXAM 3 Glen Nesse

Directions: Download this exam and answer the questions using your word processing software. You may print it, fill it in by hand, and then scan it or take photos if you’d like. If you do so, be sure that all answers are legible. When you are finished, please upload the exam to Canvas as either an MSWord document (.docx) or Adobe document (.pdf). You may upload .jpg or .jpeg if you took photos. Double check to make sure your answers are readable.

You will have the full class session to finish. If you use out-of-class sources to answer questions, you must cite the sources you have used. The test is worth 200 points.

You may copy and paste the following symbols.

Negation: ∼

Disjunction: ⌵

Conjunction: ⦁

Conditional: →

Biconditional: ↔

Conclusion Indicator: ∴

Short Answer (60 points total):

1. Successfully performing a proof on an argument tells us what about that argument?

2. From Chapter 8 of our book , what is the Law of the Excluded Middle?

3. From Chapter 8 of our book, what is the Law of Non-Contradiction?

4. Perform double negation on the following statement: T ⌵ ~~S

5. Perform either version of Material Equivalence on the following statement: (P ⦁ ∼Q) ↔ (T ⦁ ∼U)

6. Perform either version of De Morgan’s Laws on the following statement: ~(~T ⦁ ~U)

7. Perform Association on the following statement: M ⦁ [R ⦁ (S → ~M)]

8. Perform Exportation on the following statement: ~X → (~X → Y)

9. Perform Distribution on the following statement: ~A ⌵ (~B ⦁ ~C)

10. Perform Material Implication on the following statement: ~(T ⦁ ~R) ⌵ S

Implicational Rules (60 points total): Construct a proof to demonstrate that the following arguments are valid. You only need to use the eight rules of implication, but you may use the equivalence rules if you would like. (All proofs can be solved with five or less steps, but you may take more steps.)

1. N ⌵ ∼P

2. (~P → R) ⦁ ~R

∴ N

1. (A → C) → D

2. (A → ~B) ⦁ (~B → C)

∴ D

1. ~S → W

2. ~T → U

3. (~S ⌵ ~T) ⦁ ~U

∴ W

1. (B ⦁ ~N)→ X

2. Y ⌵ B

3. N → Y

4. ~ Y

∴ X ⌵ A

Implicational and Equivalence Rules (80 points total): Construct a proof to demonstrate that the following arguments are valid. You may use any of the 18 implicational and equivalence rules.

1. X ↔ ~X

∴ Y

1. ∼(∼P ⌵ ∼Q)

2. S → ∼(P ⦁ Q)

3. S ⌵ ~R

∴ ∼R

1. ∼(∼F ⦁ R) ⌵ F

2. (∼R → X) ⦁ (F → Y)

∴ X ⌵ Y

1. (T ⌵ G) ⌵ P

2. (R ⦁ T) ⌵ (R ⦁ G)

3. R ↔ ∼(T ⌵ P)

4. ∴ G