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