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