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Expresión !(!(!a*(b⊕c))*!(a*c))
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Solución
Ha introducido
[src]
¬((¬(a∧c))∧(¬((¬a)∧(b⊕c))))
$$\neg \left(\neg \left(a \wedge c\right) \wedge \neg \left(\neg a \wedge \left(b ⊕ c\right)\right)\right)$$
Вы использовали:
⊕ - Сложение по модулю 2 (Исключающее или).
Возможно вы имели ввиду символ ∨ - Дизъюнкция (ИЛИ)?
Посмотреть с символом ∨
Solución detallada
$$\neg \left(a \wedge c\right) = \neg a \vee \neg c$$
$$b ⊕ c = \left(b \wedge \neg c\right) \vee \left(c \wedge \neg b\right)$$
$$\neg a \wedge \left(b ⊕ c\right) = \neg a \wedge \left(b \vee c\right) \wedge \left(\neg b \vee \neg c\right)$$
$$\neg \left(\neg a \wedge \left(b ⊕ c\right)\right) = a \vee \left(b \wedge c\right) \vee \left(\neg b \wedge \neg c\right)$$
$$\neg \left(a \wedge c\right) \wedge \neg \left(\neg a \wedge \left(b ⊕ c\right)\right) = \left(a \wedge \neg c\right) \vee \left(\neg b \wedge \neg c\right) \vee \left(b \wedge c \wedge \neg a\right)$$
$$\neg \left(\neg \left(a \wedge c\right) \wedge \neg \left(\neg a \wedge \left(b ⊕ c\right)\right)\right) = \left(a \wedge c\right) \vee \left(c \wedge \neg b\right) \vee \left(b \wedge \neg a \wedge \neg c\right)$$
$$b ⊕ c = \left(b \wedge \neg c\right) \vee \left(c \wedge \neg b\right)$$
$$\neg a \wedge \left(b ⊕ c\right) = \neg a \wedge \left(b \vee c\right) \wedge \left(\neg b \vee \neg c\right)$$
$$\neg \left(\neg a \wedge \left(b ⊕ c\right)\right) = a \vee \left(b \wedge c\right) \vee \left(\neg b \wedge \neg c\right)$$
$$\neg \left(a \wedge c\right) \wedge \neg \left(\neg a \wedge \left(b ⊕ c\right)\right) = \left(a \wedge \neg c\right) \vee \left(\neg b \wedge \neg c\right) \vee \left(b \wedge c \wedge \neg a\right)$$
$$\neg \left(\neg \left(a \wedge c\right) \wedge \neg \left(\neg a \wedge \left(b ⊕ c\right)\right)\right) = \left(a \wedge c\right) \vee \left(c \wedge \neg b\right) \vee \left(b \wedge \neg a \wedge \neg c\right)$$
Simplificación
[src]
$$\left(a \wedge c\right) \vee \left(c \wedge \neg b\right) \vee \left(b \wedge \neg a \wedge \neg c\right)$$
(a∧c)∨(c∧(¬b))∨(b∧(¬a)∧(¬c))
Tabla de verdad
+---+---+---+--------+ | a | b | c | result | +===+===+===+========+ | 0 | 0 | 0 | 0 | +---+---+---+--------+ | 0 | 0 | 1 | 1 | +---+---+---+--------+ | 0 | 1 | 0 | 1 | +---+---+---+--------+ | 0 | 1 | 1 | 0 | +---+---+---+--------+ | 1 | 0 | 0 | 0 | +---+---+---+--------+ | 1 | 0 | 1 | 1 | +---+---+---+--------+ | 1 | 1 | 0 | 0 | +---+---+---+--------+ | 1 | 1 | 1 | 1 | +---+---+---+--------+
FND
[src]
Ya está reducido a FND
$$\left(a \wedge c\right) \vee \left(c \wedge \neg b\right) \vee \left(b \wedge \neg a \wedge \neg c\right)$$
(a∧c)∨(c∧(¬b))∨(b∧(¬a)∧(¬c))
FNC
[src]
$$\left(b \vee c\right) \wedge \left(c \vee \neg a\right) \wedge \left(c \vee \neg c\right) \wedge \left(a \vee b \vee c\right) \wedge \left(a \vee b \vee \neg b\right) \wedge \left(a \vee c \vee \neg a\right) \wedge \left(a \vee c \vee \neg c\right) \wedge \left(a \vee \neg a \vee \neg b\right) \wedge \left(a \vee \neg b \vee \neg c\right) \wedge \left(b \vee c \vee \neg b\right) \wedge \left(c \vee \neg a \vee \neg b\right) \wedge \left(c \vee \neg b \vee \neg c\right)$$
(b∨c)∧(c∨(¬a))∧(c∨(¬c))∧(a∨b∨c)∧(a∨b∨(¬b))∧(a∨c∨(¬a))∧(a∨c∨(¬c))∧(b∨c∨(¬b))∧(a∨(¬a)∨(¬b))∧(a∨(¬b)∨(¬c))∧(c∨(¬a)∨(¬b))∧(c∨(¬b)∨(¬c))
FNCD
[src]
$$\left(b \vee c\right) \wedge \left(c \vee \neg a\right) \wedge \left(a \vee \neg b \vee \neg c\right)$$
(b∨c)∧(c∨(¬a))∧(a∨(¬b)∨(¬c))
FNDP
[src]
$$\left(a \wedge c\right) \vee \left(c \wedge \neg b\right) \vee \left(b \wedge \neg a \wedge \neg c\right)$$
(a∧c)∨(c∧(¬b))∨(b∧(¬a)∧(¬c))