Practice Exam #2 -
Selected Answers
Part III Proofs: Construct proofs of one
of the following arguments. You may use conditional and indirect proof as
needed. (30 points)
1.
(A
≡ B)
⊃ C, ~(C v A), /// B
Proof:
| 1. |
(A
≡ B)
⊃ C |
premise |
| 2. |
~(C v A) |
premise |
| 3. |
~C & ~A |
DEM, 2 |
| 4. |
~C |
simp 3 |
| 5. |
~(A
≡ B) |
m.t. 1, 4 |
| 6. |
~[(A
⊃ B) & (B ⊃ A)] |
BE 5 |
| 7. |
~(A
⊃ B) v ~(B
⊃ A) |
DEM 6 |
| 8. |
~A |
simp 3 |
| 9. |
~A v B |
disj 8 |
| 10. |
(A
⊃ B) |
CE, 9 |
| 11. |
~~(A
⊃ B) |
DN, 10 |
| 12. |
~(B
⊃ A) |
d.s., 7, 11 |
| 13. |
~(~B v A) |
C.E., 12 |
| 14. |
~~B & ~A |
DEM 13 |
| 15. |
~~B |
simp, 14 |
| 16. |
B |
DN, 15 |
|