Expresión ab!c!d+(!a!b!c!d)+abcd+a!bc!d+!abc!d

Ha introducido [src]

(a∧b∧c∧d)∨(a∧b∧c∧(¬d))∨(a∧b∧(¬c)∧(¬d))∨(a∧c∧(¬b)∧(¬d))∨((¬a)∧(¬b)∧(¬c)∧(¬d))

\left(a \wedge b \wedge c \wedge d\right) \vee \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(\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 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(\neg a \wedge \neg b \wedge \neg c \wedge \neg d\right) = \left(a \vee \neg b\right) \wedge \left(a \vee \neg c\right) \wedge \left(b \vee \neg d\right) \wedge \left(c \vee \neg d\right) \wedge \left(b \vee c \vee \neg a\right)

Simplificación [src]

\left(a \vee \neg b\right) \wedge \left(a \vee \neg c\right) \wedge \left(b \vee \neg d\right) \wedge \left(c \vee \neg d\right) \wedge \left(b \vee c \vee \neg a\right)

(a∨(¬b))∧(a∨(¬c))∧(b∨(¬d))∧(c∨(¬d))∧(b∨c∨(¬a))

Tabla de verdad

+---+---+---+---+--------+
| a | b | c | d | result |
+===+===+===+===+========+
| 0 | 0 | 0 | 0 | 1      |
+---+---+---+---+--------+
| 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 | 0      |
+---+---+---+---+--------+
| 1 | 0 | 0 | 1 | 0      |
+---+---+---+---+--------+
| 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 | 1      |
+---+---+---+---+--------+

FNC [src]

Ya está reducido a FNC

\left(a \vee \neg b\right) \wedge \left(a \vee \neg c\right) \wedge \left(b \vee \neg d\right) \wedge \left(c \vee \neg d\right) \wedge \left(b \vee c \vee \neg a\right)

(a∨(¬b))∧(a∨(¬c))∧(b∨(¬d))∧(c∨(¬d))∧(b∨c∨(¬a))

FND [src]

\left(a \wedge b \wedge c\right) \vee \left(a \wedge b \wedge \neg d\right) \vee \left(a \wedge c \wedge \neg d\right) \vee \left(a \wedge \neg a \wedge \neg d\right) \vee \left(a \wedge b \wedge c \wedge \neg a\right) \vee \left(a \wedge b \wedge c \wedge \neg b\right) \vee \left(a \wedge b \wedge c \wedge \neg c\right) \vee \left(a \wedge b \wedge c \wedge \neg d\right) \vee \left(a \wedge b \wedge \neg a \wedge \neg d\right) \vee \left(a \wedge b \wedge \neg b \wedge \neg d\right) \vee \left(a \wedge b \wedge \neg c \wedge \neg d\right) \vee \left(a \wedge c \wedge \neg a \wedge \neg d\right) \vee \left(a \wedge c \wedge \neg b \wedge \neg d\right) \vee \left(a \wedge c \wedge \neg c \wedge \neg d\right) \vee \left(a \wedge \neg a \wedge \neg b \wedge \neg d\right) \vee \left(a \wedge \neg a \wedge \neg c \wedge \neg d\right) \vee \left(b \wedge c \wedge \neg b \wedge \neg c\right) \vee \left(b \wedge \neg b \wedge \neg c \wedge \neg d\right) \vee \left(c \wedge \neg b \wedge \neg c \wedge \neg d\right) \vee \left(\neg a \wedge \neg b \wedge \neg c \wedge \neg d\right) \vee \left(a \wedge b \wedge c \wedge \neg a \wedge \neg b\right) \vee \left(a \wedge b \wedge c \wedge \neg a \wedge \neg c\right) \vee \left(a \wedge b \wedge c \wedge \neg b \wedge \neg d\right) \vee \left(a \wedge b \wedge c \wedge \neg c \wedge \neg d\right) \vee \left(a \wedge b \wedge \neg a \wedge \neg b \wedge \neg d\right) \vee \left(a \wedge b \wedge \neg a \wedge \neg c \wedge \neg d\right) \vee \left(a \wedge c \wedge \neg a \wedge \neg b \wedge \neg d\right) \vee \left(a \wedge c \wedge \neg a \wedge \neg c \wedge \neg d\right) \vee \left(b \wedge c \wedge \neg a \wedge \neg b \wedge \neg c\right) \vee \left(b \wedge c \wedge \neg b \wedge \neg c \wedge \neg d\right) \vee \left(b \wedge \neg a \wedge \neg b \wedge \neg c \wedge \neg d\right) \vee \left(c \wedge \neg a \wedge \neg b \wedge \neg c \wedge \neg d\right)

(a∧b∧c)∨(a∧b∧(¬d))∨(a∧c∧(¬d))∨(a∧(¬a)∧(¬d))∨(a∧b∧c∧(¬a))∨(a∧b∧c∧(¬b))∨(a∧b∧c∧(¬c))∨(a∧b∧c∧(¬d))∨(a∧b∧(¬a)∧(¬d))∨(a∧b∧(¬b)∧(¬d))∨(a∧b∧(¬c)∧(¬d))∨(a∧c∧(¬a)∧(¬d))∨(a∧c∧(¬b)∧(¬d))∨(a∧c∧(¬c)∧(¬d))∨(b∧c∧(¬b)∧(¬c))∨(a∧(¬a)∧(¬b)∧(¬d))∨(a∧(¬a)∧(¬c)∧(¬d))∨(b∧(¬b)∧(¬c)∧(¬d))∨(c∧(¬b)∧(¬c)∧(¬d))∨(a∧b∧c∧(¬a)∧(¬b))∨(a∧b∧c∧(¬a)∧(¬c))∨(a∧b∧c∧(¬b)∧(¬d))∨(a∧b∧c∧(¬c)∧(¬d))∨((¬a)∧(¬b)∧(¬c)∧(¬d))∨(a∧b∧(¬a)∧(¬b)∧(¬d))∨(a∧b∧(¬a)∧(¬c)∧(¬d))∨(a∧c∧(¬a)∧(¬b)∧(¬d))∨(a∧c∧(¬a)∧(¬c)∧(¬d))∨(b∧c∧(¬a)∧(¬b)∧(¬c))∨(b∧c∧(¬b)∧(¬c)∧(¬d))∨(b∧(¬a)∧(¬b)∧(¬c)∧(¬d))∨(c∧(¬a)∧(¬b)∧(¬c)∧(¬d))

FNDP [src]

\left(a \wedge b \wedge c\right) \vee \left(a \wedge b \wedge \neg d\right) \vee \left(a \wedge c \wedge \neg d\right) \vee \left(\neg a \wedge \neg b \wedge \neg c \wedge \neg d\right)

(a∧b∧c)∨(a∧b∧(¬d))∨(a∧c∧(¬d))∨((¬a)∧(¬b)∧(¬c)∧(¬d))

FNCD [src]

\left(a \vee \neg b\right) \wedge \left(a \vee \neg c\right) \wedge \left(b \vee \neg d\right) \wedge \left(c \vee \neg d\right) \wedge \left(b \vee c \vee \neg a\right)

(a∨(¬b))∧(a∨(¬c))∧(b∨(¬d))∧(c∨(¬d))∧(b∨c∨(¬a))

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Expresión ab!c!d+(!a!b!c!d)+abcd+a!bc!d+!abc!d

Solución