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Lógica matemática/ ABC∨¬ABC(¬AB∨AB¬C)

Expresión ABC∨¬ABC(¬AB∨AB¬C)

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    Solución

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