Sr Examen
Lógica matemática/ CD+C¬D¬A+¬AC+A¬BC+¬A¬B¬D+¬AD+A¬BD

Expresión CD+C¬D¬A+¬AC+A¬BC+¬A¬B¬D+¬AD+A¬BD

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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