Sr Examen
Expresión A&¬B&¬Cv(¬AvB)&CvC&¬C
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
(c∧(¬c))∨(c∧(b∨(¬a)))∨(a∧(¬b)∧(¬c))
$$\left(c \wedge \neg c\right) \vee \left(c \wedge \left(b \vee \neg a\right)\right) \vee \left(a \wedge \neg b \wedge \neg c\right)$$
Solución detallada
$$c \wedge \neg c = \text{False}$$
$$\left(c \wedge \neg c\right) \vee \left(c \wedge \left(b \vee \neg a\right)\right) \vee \left(a \wedge \neg b \wedge \neg c\right) = \left(b \wedge c\right) \vee \left(c \wedge \neg a\right) \vee \left(a \wedge \neg b \wedge \neg c\right)$$
$$\left(c \wedge \neg c\right) \vee \left(c \wedge \left(b \vee \neg a\right)\right) \vee \left(a \wedge \neg b \wedge \neg c\right) = \left(b \wedge c\right) \vee \left(c \wedge \neg a\right) \vee \left(a \wedge \neg b \wedge \neg c\right)$$
Simplificación
[src]
$$\left(b \wedge c\right) \vee \left(c \wedge \neg a\right) \vee \left(a \wedge \neg b \wedge \neg c\right)$$
(b∧c)∨(c∧(¬a))∨(a∧(¬b)∧(¬c))
Tabla de verdad
+---+---+---+--------+ | a | b | c | 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 | 0 | +---+---+---+--------+ | 1 | 1 | 1 | 1 | +---+---+---+--------+
FNCD
[src]
$$\left(a \vee c\right) \wedge \left(c \vee \neg b\right) \wedge \left(b \vee \neg a \vee \neg c\right)$$
(a∨c)∧(c∨(¬b))∧(b∨(¬a)∨(¬c))
FND
[src]
Ya está reducido a FND
$$\left(b \wedge c\right) \vee \left(c \wedge \neg a\right) \vee \left(a \wedge \neg b \wedge \neg c\right)$$
(b∧c)∨(c∧(¬a))∨(a∧(¬b)∧(¬c))
FNC
[src]
$$\left(a \vee c\right) \wedge \left(c \vee \neg b\right) \wedge \left(c \vee \neg c\right) \wedge \left(a \vee b \vee c\right) \wedge \left(a \vee b \vee \neg a\right) \wedge \left(a \vee c \vee \neg a\right) \wedge \left(b \vee c \vee \neg b\right) \wedge \left(b \vee c \vee \neg c\right) \wedge \left(b \vee \neg a \vee \neg b\right) \wedge \left(b \vee \neg a \vee \neg c\right) \wedge \left(c \vee \neg a \vee \neg b\right) \wedge \left(c \vee \neg a \vee \neg c\right)$$
(a∨c)∧(c∨(¬b))∧(c∨(¬c))∧(a∨b∨c)∧(a∨b∨(¬a))∧(a∨c∨(¬a))∧(b∨c∨(¬b))∧(b∨c∨(¬c))∧(b∨(¬a)∨(¬b))∧(b∨(¬a)∨(¬c))∧(c∨(¬a)∨(¬b))∧(c∨(¬a)∨(¬c))
FNDP
[src]
$$\left(b \wedge c\right) \vee \left(c \wedge \neg a\right) \vee \left(a \wedge \neg b \wedge \neg c\right)$$
(b∧c)∨(c∧(¬a))∨(a∧(¬b)∧(¬c))