Sr Examen
Lógica matemática/ DC¬B¬A+DCBA

Expresión DC¬B¬A+DCBA

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    Solución

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