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