2.4.xa. Exercise answers
The answers below avoid the use of Cnj in order to maximize the use of the rule Adj. In some cases, a mixed use of the two would have produced a more natural argument.
| 1. |
| │A | (1) |
| ├─ | |
| 1 Adj | │A ∧ A | X,(2) |
| │● | |
| ├─ | |
| 2 QED | │A ∧ A | |
|
| 2. |
| │A ∧ B | 1 |
| │B ∧ C | 2 |
| │B ∧ D | 3 |
| ├─ | |
| 1 Ext | │A | (4) |
| 1 Ext | │B | |
| 2 Ext | │B | |
| 2 Ext | │C | |
| 3 Ext | │B | |
| 3 Ext | │D | (4) |
| 4 Adj | │A ∧ D | X,(5) |
| │● | |
| ├─ | |
| 5 QED | │A ∧ D | |
|
| 3. |
| │A ∧ B | 1 |
| ├─ | |
| 1 Ext | │A | (2),(3) |
| 1 Ext | │B | (2) |
| 2 Adj | │B ∧ A | X,(3) |
| 3 Adj | │A ∧ (B ∧ A) | X,(4) |
| │● | |
| ├─ | |
| 4 QED | │A ∧ (B ∧ A) | |
|
| 4. |
| │A | (2) |
| │B ∧ C | 1 |
| │D | |
| ├─ | |
| 1 Ext | │B | (2),(4) |
| 1 Ext | │C | (3) |
| 2 Adj | │B ∧ A | X,(3) |
| 3 Adj | │C ∧ (B ∧ A) | X,(4) |
| 4 Adj | │(C ∧ (B ∧ A)) ∧ B | X,(5) |
| │● | |
| ├─ | |
| 5 QED | │(C ∧ (B ∧ A)) ∧ B | |
|