Reference no: EM131103109

Introductory Logic

Assignment 1

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I. Construct a truth table for each of the following claims. Example:
¬ (C v D)
F T T T
F T T F
F F T T
T F F F

1. (A & ¬B)
2. ¬(C v D)
3. ¬(A --> ¬B)
4. (P ≡ (Q --> R))
5. ¬(¬W & ¬P)

II. Determine whether each pair of sentences is logically equivalent. Justify your answer with a complete or partial truth table.

Example: (A v B), (B v A)

(A v B) (B v A)
T T T T T T
T T F T T F
F T T F T T
F F F F F F

These sentences are logically equivalent because their truth tables are identical.

1. A, ¬ A

2. A, (A v A)

3. (A → A), (A ≡ A)

4. (A v ¬ B), (A → B)

5. (A v ¬ A), (¬ B ≡ B)

6. ¬ (A & B), (¬ A v ¬ B)

7. ¬ (A → B), (¬ A → ¬ B)

8. (A → B), (¬ B → ¬ A)

9. [(A v B) v C], [A v (B v C)]

10. [(A v B) & C], [A v (B & C)]

III. Construct a truth table for each of the following arguments.

1. ((P --> Q) & P) /.: Q

2. (L --> ¬L) /.: ¬L

3. (M ≡ ¬N) ; ¬(N & ¬M) /.: (M --> N)

4. (A ≡ ¬B) /.: (B v A)

5. (H --> I) ; (J ≡ H) ; (¬I v H) /.: (J ≡ I)

Assignment 2

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I. Using your answers from Assignment 5, Part III, test each of the following arguments for validity using the long truth table method.Under each argument, write "valid" or "invalid." If an argument is invalid, say which row or rows show(s) that it is invalid. (2 pts. each)

1. ((P --> Q) & P) /.: Q

2. (L -->¬L) /.: ¬L

3. (M ≡ ¬N) ;¬(N &¬M) /.: (M --> N)

4. (A ≡ ¬B) /.: (B v A)

5. (H --> I) ; (J ≡ H) ; (¬I v H) /.: (J ≡ I)

II. Determine whether each argument is valid or invalid. Justify your answer with a complete or partial truth table.

1. (A → A) /.: A

2. (A v [A → (A ≡ A)]) /.: A

3. [A → (A v ¬ A)] /.: ¬ A

4. [A ≡ ¬ (B ≡ A)] /.: A

5. [A v (B → A)] /.: (¬ A → ¬ B)

6. (A → B); B /.: A

7. (A v B); (B v C); ¬ A /.: (B & C)

8. (A v B); (B v C); ¬ A /.: (A & C)

9. [(B & A) → C]; [(C & A) → B] /.: [(C & B) → A]

10. (A ≡ B); (B ≡ C) /.: (A ≡ C)

III. Test each of the following arguments for validity using the short truth table method. Show your work here and write "valid" or "invalid." (2 pts. each)

1. (P v ¬Q) ; (R -->¬Q) /.: (¬P --> R)

2. (A v B) ; (A --> B) /.: (B -->¬A)

3. (¬(Y & O) v W) /.: (Y --> W)

4. (Y ≡ Z) ; (¬Y v ¬W) ; W /.: Z

5. (E v F) ; (E --> F) ; (C & D) /.: (F -->¬C).