2.4.x. Exercise questions
Use the basic system of derivations along with the attachment rule Adj to establish the following. These repeat entailments from earlier exercises and examples (specifically, b and d of exercise 2.2.x.2 and exercises 2 and 4 of 2.3.x). They will work best as exercises in the use of Adj if you avoid using Cnj.
| 1. | A ⊨ A ∧ A |
| 2. | A ∧ B, B ∧ C, C ∧ D ⊨ A ∧ D |
| 3. | A ∧ B ⊨ A ∧ (B ∧ A) |
| 4. | A, B ∧ C, D ⊨ (C ∧ (B ∧ A)) ∧ B |
The exercise machine doesn’t incorporate attachment rules, so, while it can generate exercises where Adj would be useful, that rule won’t be used in any answers it produces.