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