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Lógica matemática/ неА&Б&С+АнеБнеС+НеАБС

Expresión неА&Б&С+АнеБнеС+НеАБС

El profesor se sorprenderá mucho al ver tu solución correcta😉

⌨

    Solución

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