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