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