Sr Examen
Lógica matemática/ CD~A

Expresión CD~A

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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