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