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Lógica matemática/ abc+ab+de

Expresión abc+ab+de

El profesor se sorprenderá mucho al ver tu solución correcta😉

⌨

    Solución

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