Sr Examen
Lógica matemática/ С&¬a&¬b+¬С&¬a&b+¬С&a&¬b+C&b&a

Expresión С&¬a&¬b+¬С&¬a&b+¬С&a&¬b+C&b&a

El profesor se sorprenderá mucho al ver tu solución correcta😉

⌨

    Solución

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