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Lógica matemática/ Bv(A<->C)

Expresión Bv(A<->C)

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    Solución

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