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Construct a truth table for each of the given arguments
Course:- Theory of Computation
Reference No.:- EM131103109

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Introductory Logic

Assignment 1

You may write these out by hand and scan them or take a picture with your phone and upload them.

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

You may write these out by hand and scan them or take a picture with your phone and upload them.

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).

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