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