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Lógica matemática/ not(not((not(a)ornot(b))and(aorb)))

Expresión not(not((not(a)ornot(b))and(aorb)))

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    Solución

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