Answer to homework on §2.2
Construct a derivation to show: A ∧ B, (C ∧ D) ∧ E ⇒ C ∧ (B ∧ D).
(Notice that this is the same as showing that the argument
is valid. That means that your derivation should begin with the resources A ∧ B and (C ∧ D) ∧ E on separate lines.)
| off | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | on |
| │A ∧ B | 1 | |
| │(C ∧ D) ∧ E | 2 | |
| ├─ | ||
| 1 Ext | │A | (8) |
| 1 Ext | │B | (7) |
| 2 Ext | │C ∧ D | 3 |
| 2 Ext | │E | |
| 3 Ext | │C | (5) |
| 3 Ext | │D | |
| │ | ||
| ││● | ||
| │├─ | ||
| 5 QED | ││C | 4 |
| │ | ||
| │││● | ||
| ││├─ | ||
| 7 QED | │││B | 6 |
| ││ | ||
| │││● | ||
| ││├─ | ||
| 8 QED | │││D | 6 |
| │├─ | ||
| 6 Cnj | ││B ∧ D | 4 |
| ├─ | ||
| 4 Cnj | │C ∧ (B ∧ D) |