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