7.7.x. Exercise questions
Use derivations to check each of the claims below; if a derivation indicates that a claim fails, describe a structure that divides an open gap.
| 1. | Fa ⊨ ∀x Fx |
| 2. | ∀x Rxx ⊨ ∀x Rxa |
| 3. | ∀x ¬ Fx ≃ ¬ ∀x Fx |
| 4. |
No widget is a gadget No gizmo is a widget No gizmo is a gadget |
| 5. | No widget is a gadget ≃ Not every widget is a gadget |
| 6. |
Everything is either finished or unstarted Either everything is finished or everything is unstarted |
| 7. | ¬ ∀x ¬ ∀y Rxy ⊨ ∀x ¬ ∀y ¬ Rxy |
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