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Lógica matemática/ ACD+B¬CD

Expresión ACD+B¬CD

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    Solución

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