WEEK 8 :: Homework

Using ∃LOGIC construct annotated derivations showing that the following arguments are valid.


3:2 ∀x(Fx ∧ Gx) ∴ ∀xGx

3:3 ∃xFx ∴ ∃x(Gx → Fx)

3:4 ∀x(Fx→(¬Gx → Hx)) ∴ ∀x(Fx → (Gx ∨ Hx))

3:5 ∀x(Fx → Gx). ∀x(Gx → Hx) ∴ (Fa → ∃x(Gx ∧ Hx))

3:6 (∀x¬Fx → ∀xFx) ∴ ∃xFx

3:7 (∀xFx ∨ ∀xGx). ∀x(Fx → ¬Gx) ∴ ∃xFx → ∀xFx

3:8 (P → ∀x(Fx → Fa)). (∀x(Fx → Gx) ∧ ∀x(Gx → Hx)) ∴ ¬Ha → (¬P ∨ ∀x¬Fx)

3:9 ∃x(Fx ∨ Ga). ∀x(Fx → Gx) ∴ ∃xGx

3:10 ∀x(Fx → Gx) ∴ ∀x((Fx ∧ ¬∃y(Gy ∧ Hy)) → ∃x¬Hx)

3:11 ∀x(Fx↔P). ∃xFx ∴ ∀xFx

   

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