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Lógica matemática/ (¬A∧(B∨¬C))∨(D∧E)

Expresión (¬A∧(B∨¬C))∨(D∧E)

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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