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Lógica matemática/ c&(avb)v(d&¬c)

Expresión c&(avb)v(d&¬c)

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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