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Lógica matemática/ ABC+AB¬CD+¬AB¬CD+¬ABCD

Expresión ABC+AB¬CD+¬AB¬CD+¬ABCD

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    Solución

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