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Lógica matemática/ AvC⇔Bv!C

Expresión AvC⇔Bv!C

El profesor se sorprenderá mucho al ver tu solución correcta😉

⌨

    Solución

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