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