Sr Examen
Expresión zv(y⇒x),x⇒(yv¬z),y&z⇒¬x⇔zv¬x
El profesor se sorprenderá mucho al ver tu solución correcta😉
⌨
Solución
Ha introducido
[src]
(z | (Implies(y, x)), Implies(x, y | ~z), Equivalent(z | ~x, Implies(y & z, ~x)))
(Or(z, Implies(y, x)), Implies(x, Or(y, Not(z))), Equivalent(Implies(And(y, z), Not(x)), Or(z, Not(x))))
Вы использовали:
| - Не-и (штрих Шеффера).
Возможно вы имели ввиду символ ∨ - Дизъюнкция (ИЛИ)?
Посмотреть с символом ∨
Solución detallada
$$y \Rightarrow x = x \vee \neg y$$
$$z \vee \left(y \Rightarrow x\right) = x \vee z \vee \neg y$$
$$x \Rightarrow \left(y \vee \neg z\right) = y \vee \neg x \vee \neg z$$
$$\left(y \wedge z\right) \Rightarrow \neg x = \neg x \vee \neg y \vee \neg z$$
$$\left(\left(y \wedge z\right) \Rightarrow \neg x\right) ⇔ \left(z \vee \neg x\right) = \left(z \wedge \neg y\right) \vee \neg x$$
$$z \vee \left(y \Rightarrow x\right) = x \vee z \vee \neg y$$
$$x \Rightarrow \left(y \vee \neg z\right) = y \vee \neg x \vee \neg z$$
$$\left(y \wedge z\right) \Rightarrow \neg x = \neg x \vee \neg y \vee \neg z$$
$$\left(\left(y \wedge z\right) \Rightarrow \neg x\right) ⇔ \left(z \vee \neg x\right) = \left(z \wedge \neg y\right) \vee \neg x$$
Simplificación
[src]
(Or(z, Implies(y, x)), Implies(x, Or(y, Not(z))), Equivalent(Implies(And(y, z), Not(x)), Or(z, Not(x))))
(z | (Implies(y, x)), Implies(x, y | ~z), Equivalent(z | ~x, Implies(y & z, ~x)))
Tabla de verdad
+---+---+---+--------+ | x | y | z | result | +===+===+===+========+ | 0 | 0 | 0 | 1 | +---+---+---+--------+ | 0 | 0 | 1 | 1 | +---+---+---+--------+ | 0 | 1 | 0 | 1 | +---+---+---+--------+ | 0 | 1 | 1 | 1 | +---+---+---+--------+ | 1 | 0 | 0 | 1 | +---+---+---+--------+ | 1 | 0 | 1 | 1 | +---+---+---+--------+ | 1 | 1 | 0 | 1 | +---+---+---+--------+ | 1 | 1 | 1 | 1 | +---+---+---+--------+
FNDP
[src]
(Or(z, Implies(y, x)), Implies(x, Or(y, Not(z))), Equivalent(Implies(And(y, z), Not(x)), Or(z, Not(x))))
(z | (Implies(y, x)), Implies(x, y | ~z), Equivalent(z | ~x, Implies(y & z, ~x)))
FND
[src]
(Or(z, Implies(y, x)), Implies(x, Or(y, Not(z))), Equivalent(Implies(And(y, z), Not(x)), Or(z, Not(x))))
(z | (Implies(y, x)), Implies(x, y | ~z), Equivalent(z | ~x, Implies(y & z, ~x)))
FNCD
[src]
(Or(z, Implies(y, x)), Implies(x, Or(y, Not(z))), Equivalent(Implies(And(y, z), Not(x)), Or(z, Not(x))))
(z | (Implies(y, x)), Implies(x, y | ~z), Equivalent(z | ~x, Implies(y & z, ~x)))
FNC
[src]
(Or(z, Implies(y, x)), Implies(x, Or(y, Not(z))), Equivalent(Implies(And(y, z), Not(x)), Or(z, Not(x))))
(z | (Implies(y, x)), Implies(x, y | ~z), Equivalent(z | ~x, Implies(y & z, ~x)))