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Lógica matemática/ not(not(a*b+not(a)*c))

Expresión not(not(a*b+not(a)*c))

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    Solución

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