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