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