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