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))))
$$\left(\left(y \wedge z \wedge \neg x\right) \vee \neg \left(x \wedge y\right)\right) \Rightarrow \left(\neg x \vee \neg \left(\left(x \wedge y\right) \vee \neg y\right)\right)$$
Solución detallada
$$\neg \left(x \wedge y\right) = \neg x \vee \neg y$$
$$\left(y \wedge z \wedge \neg x\right) \vee \neg \left(x \wedge y\right) = \neg x \vee \neg y$$
$$\left(x \wedge y\right) \vee \neg y = x \vee \neg y$$
$$\neg \left(\left(x \wedge y\right) \vee \neg y\right) = y \wedge \neg x$$
$$\neg x \vee \neg \left(\left(x \wedge y\right) \vee \neg y\right) = \neg x$$
$$\left(\left(y \wedge z \wedge \neg x\right) \vee \neg \left(x \wedge y\right)\right) \Rightarrow \left(\neg x \vee \neg \left(\left(x \wedge y\right) \vee \neg y\right)\right) = y \vee \neg x$$
$$\left(y \wedge z \wedge \neg x\right) \vee \neg \left(x \wedge y\right) = \neg x \vee \neg y$$
$$\left(x \wedge y\right) \vee \neg y = x \vee \neg y$$
$$\neg \left(\left(x \wedge y\right) \vee \neg y\right) = y \wedge \neg x$$
$$\neg x \vee \neg \left(\left(x \wedge y\right) \vee \neg y\right) = \neg x$$
$$\left(\left(y \wedge z \wedge \neg x\right) \vee \neg \left(x \wedge y\right)\right) \Rightarrow \left(\neg x \vee \neg \left(\left(x \wedge y\right) \vee \neg y\right)\right) = y \vee \neg x$$
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 | +---+---+---+--------+