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Lógica matemática/ ((avc)&(avd))&((cv(c&b)&c)va)

Expresión ((avc)&(avd))&((cv(c&b)&c)va)

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    Solución

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