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Lógica matemática/ abcdv¬abcdva¬bcdv¬a¬bcdv¬ab¬cdv¬a¬b¬cd

Expresión abcdv¬abcdva¬bcdv¬a¬bcdv¬ab¬cdv¬a¬b¬cd

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

    Ha introducido [src] 
    (a∧b∧c∧d)∨(a∧c∧d∧(¬b))∨(b∧c∧d∧(¬a))∨(b∧d∧(¬a)∧(¬c))∨(c∧d∧(¬a)∧(¬b))∨(d∧(¬a)∧(¬b)∧(¬c))
    (a∧b∧c∧d)∨(a∧c∧d∧¬b)∨(b∧c∧d∧¬a)∨(b∧d∧¬a∧¬c)∨(c∧d∧¬a∧¬b)∨(d∧¬a∧¬b∧¬c)\left(a \wedge b \wedge c \wedge d\right) \vee \left(a \wedge c \wedge d \wedge \neg b\right) \vee \left(b \wedge c \wedge d \wedge \neg a\right) \vee \left(b \wedge d \wedge \neg a \wedge \neg c\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)
    Solución detallada
    (a∧b∧c∧d)∨(a∧c∧d∧¬b)∨(b∧c∧d∧¬a)∨(b∧d∧¬a∧¬c)∨(c∧d∧¬a∧¬b)∨(d∧¬a∧¬b∧¬c)=d∧(c∨¬a)\left(a \wedge b \wedge c \wedge d\right) \vee \left(a \wedge c \wedge d \wedge \neg b\right) \vee \left(b \wedge c \wedge d \wedge \neg a\right) \vee \left(b \wedge d \wedge \neg a \wedge \neg c\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) = d \wedge \left(c \vee \neg a\right)
    Simplificación [src]
    d∧(c∨¬a)d \wedge \left(c \vee \neg a\right) 
    d∧(c∨(¬a))
    Tabla de verdad 
    +---+---+---+---+--------+
| a | b | c | d | result |
+===+===+===+===+========+
| 0 | 0 | 0 | 0 | 0      |
+---+---+---+---+--------+
| 0 | 0 | 0 | 1 | 1      |
+---+---+---+---+--------+
| 0 | 0 | 1 | 0 | 0      |
+---+---+---+---+--------+
| 0 | 0 | 1 | 1 | 1      |
+---+---+---+---+--------+
| 0 | 1 | 0 | 0 | 0      |
+---+---+---+---+--------+
| 0 | 1 | 0 | 1 | 1      |
+---+---+---+---+--------+
| 0 | 1 | 1 | 0 | 0      |
+---+---+---+---+--------+
| 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 | 0      |
+---+---+---+---+--------+
| 1 | 1 | 1 | 0 | 0      |
+---+---+---+---+--------+
| 1 | 1 | 1 | 1 | 1      |
+---+---+---+---+--------+
    FNDP [src]
    (c∧d)∨(d∧¬a)\left(c \wedge d\right) \vee \left(d \wedge \neg a\right) 
    (c∧d)∨(d∧(¬a))
    FNC [src]
    Ya está reducido a FNC
    d∧(c∨¬a)d \wedge \left(c \vee \neg a\right) 
    d∧(c∨(¬a))
    FND [src]
    (c∧d)∨(d∧¬a)\left(c \wedge d\right) \vee \left(d \wedge \neg a\right) 
    (c∧d)∨(d∧(¬a))
    FNCD [src]
    d∧(c∨¬a)d \wedge \left(c \vee \neg a\right) 
    d∧(c∨(¬a))
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