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