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