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Lógica matemática/ ¬a&¬b&¬cv¬a&¬b&cv¬a&b&cva&¬b&¬cva&¬b&cva&b&¬c

Expresión ¬a&¬b&¬cv¬a&¬b&cv¬a&b&cva&¬b&¬cva&¬b&cva&b&¬c

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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