Sr Examen
Expresión ¬(a∧b∧¬c)∧¬(¬a∧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∧(¬a)))
$$\neg \left(a \wedge b \wedge \neg c\right) \wedge \neg \left(b \wedge c \wedge \neg a\right)$$
Solución detallada
$$\neg \left(a \wedge b \wedge \neg c\right) = c \vee \neg a \vee \neg b$$
$$\neg \left(b \wedge c \wedge \neg a\right) = a \vee \neg b \vee \neg c$$
$$\neg \left(a \wedge b \wedge \neg c\right) \wedge \neg \left(b \wedge c \wedge \neg a\right) = \left(a \wedge c\right) \vee \left(\neg a \wedge \neg c\right) \vee \neg b$$
$$\neg \left(b \wedge c \wedge \neg a\right) = a \vee \neg b \vee \neg c$$
$$\neg \left(a \wedge b \wedge \neg c\right) \wedge \neg \left(b \wedge c \wedge \neg a\right) = \left(a \wedge c\right) \vee \left(\neg a \wedge \neg c\right) \vee \neg b$$
Simplificación
[src]
$$\left(a \wedge c\right) \vee \left(\neg a \wedge \neg c\right) \vee \neg b$$
(¬b)∨(a∧c)∨((¬a)∧(¬c))
Tabla de verdad
+---+---+---+--------+ | a | b | c | result | +===+===+===+========+ | 0 | 0 | 0 | 1 | +---+---+---+--------+ | 0 | 0 | 1 | 1 | +---+---+---+--------+ | 0 | 1 | 0 | 1 | +---+---+---+--------+ | 0 | 1 | 1 | 0 | +---+---+---+--------+ | 1 | 0 | 0 | 1 | +---+---+---+--------+ | 1 | 0 | 1 | 1 | +---+---+---+--------+ | 1 | 1 | 0 | 0 | +---+---+---+--------+ | 1 | 1 | 1 | 1 | +---+---+---+--------+
FNCD
[src]
$$\left(a \vee \neg b \vee \neg c\right) \wedge \left(c \vee \neg a \vee \neg b\right)$$
(a∨(¬b)∨(¬c))∧(c∨(¬a)∨(¬b))
FND
[src]
Ya está reducido a FND
$$\left(a \wedge c\right) \vee \left(\neg a \wedge \neg c\right) \vee \neg b$$
(¬b)∨(a∧c)∨((¬a)∧(¬c))
FNDP
[src]
$$\left(a \wedge c\right) \vee \left(\neg a \wedge \neg c\right) \vee \neg b$$
(¬b)∨(a∧c)∨((¬a)∧(¬c))
FNC
[src]
$$\left(a \vee \neg a \vee \neg b\right) \wedge \left(a \vee \neg b \vee \neg c\right) \wedge \left(c \vee \neg a \vee \neg b\right) \wedge \left(c \vee \neg b \vee \neg c\right)$$
(a∨(¬a)∨(¬b))∧(a∨(¬b)∨(¬c))∧(c∨(¬a)∨(¬b))∧(c∨(¬b)∨(¬c))