Lógica II - Práctica 4

“LÓGICA II”
PRÁCTICA 4
DEDUCCIÓN NATURAL (3): CUANTIFICACIÓN MÚLTIPLE
2.57
∀x∀y∀z Fxyz ├ ∀z∀y∀x Fxyz
2.58
∀x∃y∀z Fxyz ├ ∀x∀z∃y Fxyz
2.59
∃x∃y∀z Fxyz ├ ∀z∃y∃x Fxyz
2.60
∃x (Fx ∧ ∀y (Gy → Jxy)), ∀x (Fx → ¬∃y (Hy ∧ Jxy)) ├ ∀x (Gx → ¬Hx)
2.61
∃x (Fx ∧ Gx), ∃x (Fx ∧ ¬∃y (Gy ∧ Hxy)) ├ ∃x (Fx ∧ ¬∀y (Fy → Hyx))
2.62
∀x (Fx → ∀y (Hy ∧ Jy → Gxy)), ∃x (Fx ∧ ¬Gxa), Ha ├ ¬Ja
2.63
∀x (Fx → Gx), ∃x (Hx ∧ ¬∃y (Gy ∧ Jxy)) ├ ∃x (Hx ∧ ¬∃y (Fy ∧ Jxy))
2.64
∀x (Fx → ∀y (Hy → Gxy)), ∃x (Hx ∧ Gxa), Fa ├ ∃x (Gax ∧ Gxa)
2.65
∀x (Fx → Gx), ∃x (Hx ∧ Fx), ∀x (Hx → ∃y Jyx)
├ ∃x (∃y (Hy ∧ Jxy) ∧ ∃y (Gy ∧ Jxy))
1