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