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