Sr Examen
Expresión (A⊕B^C)^((B^C)⊕(B⊕C))
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
(a⊕(b∧c))∧(b⊕c⊕(b∧c))
$$\left(a ⊕ \left(b \wedge c\right)\right) \wedge \left(b ⊕ c ⊕ \left(b \wedge c\right)\right)$$
Вы использовали:
⊕ - Сложение по модулю 2 (Исключающее или).
Возможно вы имели ввиду символ ∨ - Дизъюнкция (ИЛИ)?
Посмотреть с символом ∨
Solución detallada
$$a ⊕ \left(b \wedge c\right) = \left(a \wedge \neg b\right) \vee \left(a \wedge \neg c\right) \vee \left(b \wedge c \wedge \neg a\right)$$
$$b ⊕ c ⊕ \left(b \wedge c\right) = b \vee c$$
$$\left(a ⊕ \left(b \wedge c\right)\right) \wedge \left(b ⊕ c ⊕ \left(b \wedge c\right)\right) = \left(a \vee b\right) \wedge \left(a \vee c\right) \wedge \left(b \vee c\right) \wedge \left(\neg a \vee \neg b \vee \neg c\right)$$
$$b ⊕ c ⊕ \left(b \wedge c\right) = b \vee c$$
$$\left(a ⊕ \left(b \wedge c\right)\right) \wedge \left(b ⊕ c ⊕ \left(b \wedge c\right)\right) = \left(a \vee b\right) \wedge \left(a \vee c\right) \wedge \left(b \vee c\right) \wedge \left(\neg a \vee \neg b \vee \neg c\right)$$
Simplificación
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$$\left(a \vee b\right) \wedge \left(a \vee c\right) \wedge \left(b \vee c\right) \wedge \left(\neg a \vee \neg b \vee \neg c\right)$$
(a∨b)∧(a∨c)∧(b∨c)∧((¬a)∨(¬b)∨(¬c))
Tabla de verdad
+---+---+---+--------+ | a | b | c | result | +===+===+===+========+ | 0 | 0 | 0 | 0 | +---+---+---+--------+ | 0 | 0 | 1 | 0 | +---+---+---+--------+ | 0 | 1 | 0 | 0 | +---+---+---+--------+ | 0 | 1 | 1 | 1 | +---+---+---+--------+ | 1 | 0 | 0 | 0 | +---+---+---+--------+ | 1 | 0 | 1 | 1 | +---+---+---+--------+ | 1 | 1 | 0 | 1 | +---+---+---+--------+ | 1 | 1 | 1 | 0 | +---+---+---+--------+
FND
[src]
$$\left(a \wedge b \wedge \neg a\right) \vee \left(a \wedge b \wedge \neg b\right) \vee \left(a \wedge b \wedge \neg c\right) \vee \left(a \wedge c \wedge \neg a\right) \vee \left(a \wedge c \wedge \neg b\right) \vee \left(a \wedge c \wedge \neg c\right) \vee \left(b \wedge c \wedge \neg a\right) \vee \left(b \wedge c \wedge \neg b\right) \vee \left(b \wedge c \wedge \neg c\right) \vee \left(a \wedge b \wedge c \wedge \neg a\right) \vee \left(a \wedge b \wedge c \wedge \neg b\right) \vee \left(a \wedge b \wedge c \wedge \neg c\right)$$
(a∧b∧(¬a))∨(a∧b∧(¬b))∨(a∧b∧(¬c))∨(a∧c∧(¬a))∨(a∧c∧(¬b))∨(a∧c∧(¬c))∨(b∧c∧(¬a))∨(b∧c∧(¬b))∨(b∧c∧(¬c))∨(a∧b∧c∧(¬a))∨(a∧b∧c∧(¬b))∨(a∧b∧c∧(¬c))
FNC
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Ya está reducido a FNC
$$\left(a \vee b\right) \wedge \left(a \vee c\right) \wedge \left(b \vee c\right) \wedge \left(\neg a \vee \neg b \vee \neg c\right)$$
(a∨b)∧(a∨c)∧(b∨c)∧((¬a)∨(¬b)∨(¬c))
FNDP
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$$\left(a \wedge b \wedge \neg c\right) \vee \left(a \wedge c \wedge \neg b\right) \vee \left(b \wedge c \wedge \neg a\right)$$
(a∧b∧(¬c))∨(a∧c∧(¬b))∨(b∧c∧(¬a))
FNCD
[src]
$$\left(a \vee b\right) \wedge \left(a \vee c\right) \wedge \left(b \vee c\right) \wedge \left(\neg a \vee \neg b \vee \neg c\right)$$
(a∨b)∧(a∨c)∧(b∨c)∧((¬a)∨(¬b)∨(¬c))