Sr Examen
Lógica matemática/ avbvc->d&f&g

Expresión avbvc->d&f&g

El profesor se sorprenderá mucho al ver tu solución correcta😉

⌨

    Solución

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