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Lógica matemática/ ((!a)&b&c)v(a&b&(!c))

Expresión ((!a)&b&c)v(a&b&(!c))

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    Solución

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