2.3.x. Exercise questions
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Use the basic system of derivations to check each of the claims below; if a derivation indicates that a claim fails, present a counterexample (that is, give an interpretation that divides an open gap and calculate truth values for the premises and conclusion from it—as is done in the example in 2.3.5, though you need only provide a single counterexample even when the derivation leads you to several): |
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| 1. | A ⊨ A ∧ B |
| 2. | A ∧ B ⊨ A ∧ (B ∧ A) |
| 3. | B ∧ E, C ∧ ⊤ ⊨ (A ∧ B) ∧ (C ∧ D) |
| 4. | A ∧ B, B ∧ C, C ∧ D ⊨ A ∧ D |
| 5. | A, B ∧ A, D ⊨ B ∧ ((C ∧ A) ∧ D) |
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