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