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