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Lógica matemática/ (abce)v(bcd)v(bf)

Expresión (abce)v(bcd)v(bf)

El profesor se sorprenderá mucho al ver tu solución correcta😉

⌨

    Solución

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