Sr Examen
Expresión (x->y)(y->z)(z->u)
El profesor se sorprenderá mucho al ver tu solución correcta😉
⌨
Solución
Ha introducido
[src]
(x⇒y)∧(y⇒z)∧(z⇒u)
$$\left(x \Rightarrow y\right) \wedge \left(y \Rightarrow z\right) \wedge \left(z \Rightarrow u\right)$$
Solución detallada
$$x \Rightarrow y = y \vee \neg x$$
$$y \Rightarrow z = z \vee \neg y$$
$$z \Rightarrow u = u \vee \neg z$$
$$\left(x \Rightarrow y\right) \wedge \left(y \Rightarrow z\right) \wedge \left(z \Rightarrow u\right) = \left(u \vee \neg z\right) \wedge \left(y \vee \neg x\right) \wedge \left(z \vee \neg y\right)$$
$$y \Rightarrow z = z \vee \neg y$$
$$z \Rightarrow u = u \vee \neg z$$
$$\left(x \Rightarrow y\right) \wedge \left(y \Rightarrow z\right) \wedge \left(z \Rightarrow u\right) = \left(u \vee \neg z\right) \wedge \left(y \vee \neg x\right) \wedge \left(z \vee \neg y\right)$$
Simplificación
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$$\left(u \vee \neg z\right) \wedge \left(y \vee \neg x\right) \wedge \left(z \vee \neg y\right)$$
(u∨(¬z))∧(y∨(¬x))∧(z∨(¬y))
Tabla de verdad
+---+---+---+---+--------+ | u | x | y | z | result | +===+===+===+===+========+ | 0 | 0 | 0 | 0 | 1 | +---+---+---+---+--------+ | 0 | 0 | 0 | 1 | 0 | +---+---+---+---+--------+ | 0 | 0 | 1 | 0 | 0 | +---+---+---+---+--------+ | 0 | 0 | 1 | 1 | 0 | +---+---+---+---+--------+ | 0 | 1 | 0 | 0 | 0 | +---+---+---+---+--------+ | 0 | 1 | 0 | 1 | 0 | +---+---+---+---+--------+ | 0 | 1 | 1 | 0 | 0 | +---+---+---+---+--------+ | 0 | 1 | 1 | 1 | 0 | +---+---+---+---+--------+ | 1 | 0 | 0 | 0 | 1 | +---+---+---+---+--------+ | 1 | 0 | 0 | 1 | 1 | +---+---+---+---+--------+ | 1 | 0 | 1 | 0 | 0 | +---+---+---+---+--------+ | 1 | 0 | 1 | 1 | 1 | +---+---+---+---+--------+ | 1 | 1 | 0 | 0 | 0 | +---+---+---+---+--------+ | 1 | 1 | 0 | 1 | 0 | +---+---+---+---+--------+ | 1 | 1 | 1 | 0 | 0 | +---+---+---+---+--------+ | 1 | 1 | 1 | 1 | 1 | +---+---+---+---+--------+
FNC
[src]
Ya está reducido a FNC
$$\left(u \vee \neg z\right) \wedge \left(y \vee \neg x\right) \wedge \left(z \vee \neg y\right)$$
(u∨(¬z))∧(y∨(¬x))∧(z∨(¬y))
FNCD
[src]
$$\left(u \vee \neg z\right) \wedge \left(y \vee \neg x\right) \wedge \left(z \vee \neg y\right)$$
(u∨(¬z))∧(y∨(¬x))∧(z∨(¬y))
FND
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$$\left(u \wedge y \wedge z\right) \vee \left(u \wedge y \wedge \neg y\right) \vee \left(u \wedge z \wedge \neg x\right) \vee \left(u \wedge \neg x \wedge \neg y\right) \vee \left(y \wedge z \wedge \neg z\right) \vee \left(y \wedge \neg y \wedge \neg z\right) \vee \left(z \wedge \neg x \wedge \neg z\right) \vee \left(\neg x \wedge \neg y \wedge \neg z\right)$$
(u∧y∧z)∨(u∧y∧(¬y))∨(u∧z∧(¬x))∨(y∧z∧(¬z))∨(u∧(¬x)∧(¬y))∨(y∧(¬y)∧(¬z))∨(z∧(¬x)∧(¬z))∨((¬x)∧(¬y)∧(¬z))
FNDP
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$$\left(u \wedge y \wedge z\right) \vee \left(u \wedge \neg x \wedge \neg y\right) \vee \left(\neg x \wedge \neg y \wedge \neg z\right)$$
(u∧y∧z)∨(u∧(¬x)∧(¬y))∨((¬x)∧(¬y)∧(¬z))