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Lógica matemática/ (((¬(a∨b)∧(a∨c))∧¬b)∨¬a)

Expresión (((¬(a∨b)∧(a∨c))∧¬b)∨¬a)

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    Solución

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