Sr Examen
Lógica matemática/ ab¬c¬d+ab¬cd+a¬b¬cd+a¬b¬c¬d+a¬bcd+a¬bc¬d+¬abc¬d+¬abcd+¬a¬bcd+¬a¬bc¬d

Expresión ab¬c¬d+ab¬cd+a¬b¬cd+a¬b¬c¬d+a¬bcd+a¬bc¬d+¬abc¬d+¬abcd+¬a¬bcd+¬a¬bc¬d

El profesor se sorprenderá mucho al ver tu solución correcta😉

⌨

    Solución

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