Sr Examen
Expresión ¬((¬x&(y&z))&(¬xv¬y))&xv(y&¬z)
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
(y∧(¬z))∨(x∧(¬(y∧z∧(¬x)∧((¬x)∨(¬y)))))
$$\left(x \wedge \neg \left(y \wedge z \wedge \neg x \wedge \left(\neg x \vee \neg y\right)\right)\right) \vee \left(y \wedge \neg z\right)$$
Solución detallada
$$y \wedge z \wedge \neg x \wedge \left(\neg x \vee \neg y\right) = y \wedge z \wedge \neg x$$
$$\neg \left(y \wedge z \wedge \neg x \wedge \left(\neg x \vee \neg y\right)\right) = x \vee \neg y \vee \neg z$$
$$x \wedge \neg \left(y \wedge z \wedge \neg x \wedge \left(\neg x \vee \neg y\right)\right) = x$$
$$\left(x \wedge \neg \left(y \wedge z \wedge \neg x \wedge \left(\neg x \vee \neg y\right)\right)\right) \vee \left(y \wedge \neg z\right) = x \vee \left(y \wedge \neg z\right)$$
$$\neg \left(y \wedge z \wedge \neg x \wedge \left(\neg x \vee \neg y\right)\right) = x \vee \neg y \vee \neg z$$
$$x \wedge \neg \left(y \wedge z \wedge \neg x \wedge \left(\neg x \vee \neg y\right)\right) = x$$
$$\left(x \wedge \neg \left(y \wedge z \wedge \neg x \wedge \left(\neg x \vee \neg y\right)\right)\right) \vee \left(y \wedge \neg z\right) = x \vee \left(y \wedge \neg z\right)$$
Tabla de verdad
+---+---+---+--------+ | x | y | z | result | +===+===+===+========+ | 0 | 0 | 0 | 0 | +---+---+---+--------+ | 0 | 0 | 1 | 0 | +---+---+---+--------+ | 0 | 1 | 0 | 1 | +---+---+---+--------+ | 0 | 1 | 1 | 0 | +---+---+---+--------+ | 1 | 0 | 0 | 1 | +---+---+---+--------+ | 1 | 0 | 1 | 1 | +---+---+---+--------+ | 1 | 1 | 0 | 1 | +---+---+---+--------+ | 1 | 1 | 1 | 1 | +---+---+---+--------+