Sr Examen
Expresión (¬zyv¬yz)xvyz
El profesor se sorprenderá mucho al ver tu solución correcta😉
⌨
Solución
Ha introducido
[src]
(y∧z)∨(x∧((y∧(¬z))∨(z∧(¬y))))
$$\left(x \wedge \left(\left(y \wedge \neg z\right) \vee \left(z \wedge \neg y\right)\right)\right) \vee \left(y \wedge z\right)$$
Solución detallada
$$x \wedge \left(\left(y \wedge \neg z\right) \vee \left(z \wedge \neg y\right)\right) = x \wedge \left(y \vee z\right) \wedge \left(\neg y \vee \neg z\right)$$
$$\left(x \wedge \left(\left(y \wedge \neg z\right) \vee \left(z \wedge \neg y\right)\right)\right) \vee \left(y \wedge z\right) = \left(x \wedge y\right) \vee \left(x \wedge z\right) \vee \left(y \wedge z\right)$$
$$\left(x \wedge \left(\left(y \wedge \neg z\right) \vee \left(z \wedge \neg y\right)\right)\right) \vee \left(y \wedge z\right) = \left(x \wedge y\right) \vee \left(x \wedge z\right) \vee \left(y \wedge z\right)$$
Simplificación
[src]
$$\left(x \wedge y\right) \vee \left(x \wedge z\right) \vee \left(y \wedge z\right)$$
(x∧y)∨(x∧z)∨(y∧z)
Tabla de verdad
+---+---+---+--------+ | x | y | z | result | +===+===+===+========+ | 0 | 0 | 0 | 0 | +---+---+---+--------+ | 0 | 0 | 1 | 0 | +---+---+---+--------+ | 0 | 1 | 0 | 0 | +---+---+---+--------+ | 0 | 1 | 1 | 1 | +---+---+---+--------+ | 1 | 0 | 0 | 0 | +---+---+---+--------+ | 1 | 0 | 1 | 1 | +---+---+---+--------+ | 1 | 1 | 0 | 1 | +---+---+---+--------+ | 1 | 1 | 1 | 1 | +---+---+---+--------+
FNC
[src]
$$\left(x \vee y\right) \wedge \left(x \vee z\right) \wedge \left(y \vee z\right) \wedge \left(x \vee y \vee z\right)$$
(x∨y)∧(x∨z)∧(y∨z)∧(x∨y∨z)
FND
[src]
Ya está reducido a FND
$$\left(x \wedge y\right) \vee \left(x \wedge z\right) \vee \left(y \wedge z\right)$$
(x∧y)∨(x∧z)∨(y∧z)
FNCD
[src]
$$\left(x \vee y\right) \wedge \left(x \vee z\right) \wedge \left(y \vee z\right)$$
(x∨y)∧(x∨z)∧(y∨z)
FNDP
[src]
$$\left(x \wedge y\right) \vee \left(x \wedge z\right) \vee \left(y \wedge z\right)$$
(x∧y)∨(x∧z)∨(y∧z)