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