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Lógica matemática/ C=(¬A&¬B)∨(A&B)

Expresión C=(¬A&¬B)∨(A&B)

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

    Ha introducido [src] 
    c⇔((a∧b)∨((¬a)∧(¬b)))
    c⇔((a∧b)∨(¬a∧¬b))c ⇔ \left(\left(a \wedge b\right) \vee \left(\neg a \wedge \neg b\right)\right)
    Solución detallada
    c⇔((a∧b)∨(¬a∧¬b))=(a∧b∧c)∨(a∧¬b∧¬c)∨(b∧¬a∧¬c)∨(c∧¬a∧¬b)c ⇔ \left(\left(a \wedge b\right) \vee \left(\neg a \wedge \neg b\right)\right) = \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]
    (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) 
    (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]
    (a∨¬a)∧(b∨¬b)∧(c∨¬c)∧(a∨b∨c)∧(a∨b∨¬a)∧(a∨b∨¬b)∧(a∨c∨¬a)∧(a∨c∨¬c)∧(a∨¬a∨¬b)∧(a∨¬a∨¬c)∧(a∨¬b∨¬c)∧(b∨c∨¬b)∧(b∨c∨¬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)∧(a∨¬a∨¬b∨¬c)∧(b∨c∨¬a∨¬b)∧(b∨c∨¬a∨¬c)∧(b∨c∨¬b∨¬c)∧(b∨¬a∨¬b∨¬c)∧(c∨¬a∨¬b∨¬c)\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))
    FNCD [src]
    (a∨b∨c)∧(a∨¬b∨¬c)∧(b∨¬a∨¬c)∧(c∨¬a∨¬b)\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))
    FND [src]
    Ya está reducido a FND
    (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) 
    (a∧b∧c)∨(a∧(¬b)∧(¬c))∨(b∧(¬a)∧(¬c))∨(c∧(¬a)∧(¬b))
    FNDP [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) 
    (a∧b∧c)∨(a∧(¬b)∧(¬c))∨(b∧(¬a)∧(¬c))∨(c∧(¬a)∧(¬b))
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