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