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Lógica matemática/ av¬(av¬b)∧u

Expresión av¬(av¬b)∧u

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    Solución

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