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