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Lógica matemática/ av(b&c&(avc))=(avc)&(avc)

Expresión av(b&c&(avc))=(avc)&(avc)

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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