PHL 410 Textbook Exercises 6.7.2

Textbook Exercises 6.7.2

Prove the following problems for practice. Here the uppercase letters indicate particular assertions that represent arguments that could be given in ordinary language. Rather than “translate” these arguments from ordinary language to start, we will simply begin with them represented in standard form.

1. C | D, C ∴ ¬D ∨ E

1. C | D 2. C ∴ ¬D ∨ E

3. ¬D ∨ E | D 2, Add

4.

2. (F ⊃ G) | (¬G ⊃ C) ∴ F ⊃ ¬C

3. ¬D ∴ C ⊃ ¬D

4. (¬F ⊃ ¬G) ⊃ ¬L ∴ L ⊃ G

5. ∴ [A ∨ (¬A ∧ C)] ≡ (A ∨ C)

6. A ⊃ (Z ∧ Z), ¬A ⊃ Z ∴ Z

7. C ⊃ (D ∨ ¬(A ∨ B)), ¬A ⊃ B ∴¬D ⊃ ¬C

8. A ∧ (B ⊃ C), ¬(C ∧ A) ∴ ¬B

9. D ⊃ B, D ⊃ (B ⊃ W), B ⊃ (W ⊃ S) ∴ D ⊃ S

10. J ⊃ R, (¬R ⊃ S) ⊃ D, ¬D ∴ ¬J