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Lógica matemática/ ¬(a∨b)∨c∧b

Expresión ¬(a∨b)∨c∧b

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    Solución

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