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Lógica matemática/ ABC'D'E'F'+ABEF+ABCF+ABCDE

Expresión ABC'D'E'F'+ABEF+ABCF+ABCDE

El profesor se sorprenderá mucho al ver tu solución correcta😉

⌨

    Solución

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