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