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Lógica matemática/ abc+¬a¬bcd+bc¬d+¬ab¬c+¬ab¬d

Expresión abc+¬a¬bcd+bc¬d+¬ab¬c+¬ab¬d

El profesor se sorprenderá mucho al ver tu solución correcta😉

⌨

    Solución

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