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