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Lógica matemática/ abdefvcbdef

Expresión abdefvcbdef

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⌨

    Solución

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