Sr Examen
Expresión ¬(x(y¬zvx¬z))
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Solución
Ha introducido
[src]
¬(x∧((x∧(¬z))∨(y∧(¬z))))
$$\neg \left(x \wedge \left(\left(x \wedge \neg z\right) \vee \left(y \wedge \neg z\right)\right)\right)$$
Solución detallada
$$\left(x \wedge \neg z\right) \vee \left(y \wedge \neg z\right) = \neg z \wedge \left(x \vee y\right)$$
$$x \wedge \left(\left(x \wedge \neg z\right) \vee \left(y \wedge \neg z\right)\right) = x \wedge \neg z$$
$$\neg \left(x \wedge \left(\left(x \wedge \neg z\right) \vee \left(y \wedge \neg z\right)\right)\right) = z \vee \neg x$$
$$x \wedge \left(\left(x \wedge \neg z\right) \vee \left(y \wedge \neg z\right)\right) = x \wedge \neg z$$
$$\neg \left(x \wedge \left(\left(x \wedge \neg z\right) \vee \left(y \wedge \neg z\right)\right)\right) = z \vee \neg x$$
Tabla de verdad
+---+---+---+--------+ | x | y | z | result | +===+===+===+========+ | 0 | 0 | 0 | 1 | +---+---+---+--------+ | 0 | 0 | 1 | 1 | +---+---+---+--------+ | 0 | 1 | 0 | 1 | +---+---+---+--------+ | 0 | 1 | 1 | 1 | +---+---+---+--------+ | 1 | 0 | 0 | 0 | +---+---+---+--------+ | 1 | 0 | 1 | 1 | +---+---+---+--------+ | 1 | 1 | 0 | 0 | +---+---+---+--------+ | 1 | 1 | 1 | 1 | +---+---+---+--------+