Sr Examen
Expresión ¬(AvB)∧¬(BvC)∧¬(CvD)∧¬(¬A∧¬B∧C∧D)
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
(¬(a∨b))∧(¬(b∨c))∧(¬(c∨d))∧(¬(c∧d∧(¬a)∧(¬b)))
$$\neg \left(c \wedge d \wedge \neg a \wedge \neg b\right) \wedge \neg \left(a \vee b\right) \wedge \neg \left(b \vee c\right) \wedge \neg \left(c \vee d\right)$$
Solución detallada
$$\neg \left(a \vee b\right) = \neg a \wedge \neg b$$
$$\neg \left(b \vee c\right) = \neg b \wedge \neg c$$
$$\neg \left(c \vee d\right) = \neg c \wedge \neg d$$
$$\neg \left(c \wedge d \wedge \neg a \wedge \neg b\right) = a \vee b \vee \neg c \vee \neg d$$
$$\neg \left(c \wedge d \wedge \neg a \wedge \neg b\right) \wedge \neg \left(a \vee b\right) \wedge \neg \left(b \vee c\right) \wedge \neg \left(c \vee d\right) = \neg a \wedge \neg b \wedge \neg c \wedge \neg d$$
$$\neg \left(b \vee c\right) = \neg b \wedge \neg c$$
$$\neg \left(c \vee d\right) = \neg c \wedge \neg d$$
$$\neg \left(c \wedge d \wedge \neg a \wedge \neg b\right) = a \vee b \vee \neg c \vee \neg d$$
$$\neg \left(c \wedge d \wedge \neg a \wedge \neg b\right) \wedge \neg \left(a \vee b\right) \wedge \neg \left(b \vee c\right) \wedge \neg \left(c \vee d\right) = \neg a \wedge \neg b \wedge \neg c \wedge \neg d$$
Tabla de verdad
+---+---+---+---+--------+ | a | b | c | d | result | +===+===+===+===+========+ | 0 | 0 | 0 | 0 | 1 | +---+---+---+---+--------+ | 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 | 0 | +---+---+---+---+--------+ | 0 | 1 | 1 | 1 | 0 | +---+---+---+---+--------+ | 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 | 0 | +---+---+---+---+--------+ | 1 | 1 | 1 | 1 | 0 | +---+---+---+---+--------+
FNC
[src]
Ya está reducido a FNC
$$\neg a \wedge \neg b \wedge \neg c \wedge \neg d$$
(¬a)∧(¬b)∧(¬c)∧(¬d)
FND
[src]
Ya está reducido a FND
$$\neg a \wedge \neg b \wedge \neg c \wedge \neg d$$
(¬a)∧(¬b)∧(¬c)∧(¬d)