Se selecciono un ejercicio del libro Lean Symbolic Logic de Lewis Carroll
Los enunciados son los siguientes:
Texto
Bores are dreaded;
No bore is ever begged to prolong his visit.
No one, who is dreaded, is ever begged to prolong his visit.
No bore is ever begged to prolong his visit.
No one, who is dreaded, is ever begged to prolong his visit.
A(x): Bores
∴∃(x)B(x)→¬C(x)
B(X):Dreaded
C(X):Begged to prolong his visits
Cuantores:
∀: Cuantificador Universal Todos, para todos
∃: Cuantificador Existencial Por lo menos uno, algunos, algunas
∃: Cuantificador Existencial Por lo menos uno, algunos, algunas
Se sustituira los enunciados con cuantores lógicos y usando las expresiones.
- Bores are dreaded = ∀A(x)→B(x)
- No bore is ever begged to prolong his visit .=¬A(x)→C(x)
- No one, who is dreaded, is ever begged to prolong his visit. =: ¬B(x)→C(x)
Conclusion:
Some dreaded persons are not begged to prolong their visits.∴∃(x)B(x)→¬C(x)