Translation, Validity and
Proof in PL
Solution, Question 2
2. Edson listens to "Love Supreme" just in case Elwin enjoys Miles Davis. If Elwin doesn't enjoy Miles Davis, then Doris digs Django. But if Doris digs Django, then Linda likes Luciano. Since Linda doesn't like Luciano, but Edson does listen to "Love Supreme," it follows that Elwin enjoys Miles Davis.
E: Edson listens to "Love Supreme".
M: Edwin enjoys Miles.
D: Doris digs Django.
L: Linda likes Luciano.
Translation:
E
≡ M
~M
⊃ D
D
⊃ L
~L & E
M
The argument is valid. (Check with truth tree).
Proof:
| 1. | E ≡ M | premise | ||
| 2. | ~M ⊃ D | premise | ||
| 3. | D ⊃ L | premise | ||
| 4. | ~L & E | premise | ||
| 5. | ~M | assump, ip | sp1 | |
| 6. | D | mp | 2,5 | sp1 |
| 7. | L | mp | 3,6 | sp1 |
| 8. | ~L | simp | 4 | sp1 |
| 9. | L & ~L | conj | 7,8 | sp1 |
| 10. | M | ip | 5-9 |