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