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