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Lógica matemática/ ¬(¬((A∨B)∧C))∨¬(¬((a∧b)∨(b∧C)))

Expresión ¬(¬((A∨B)∧C))∨¬(¬((a∧b)∨(b∧C)))

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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