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Lógica matemática/ (AvB)&(BvC)&(AvC)⇒A&B&C

Expresión (AvB)&(BvC)&(AvC)⇒A&B&C

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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