Phi 270
Fall 2013
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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.

Glen Helman 01 Aug 2013