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