Sr Examen
Lógica matemática/ A∨(B∧(C∨¬D))∨((D∨E)∧(E∨F∨G))

Expresión A∨(B∧(C∨¬D))∨((D∨E)∧(E∨F∨G))

El profesor se sorprenderá mucho al ver tu solución correcta😉

⌨

    Solución

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