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