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