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Lógica matemática/ �b*�c+a*b*c+a*�b+�a*b*�c+�b*c

Expresión �b*�c+a*b*c+a*�b+�a*b*�c+�b*c

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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