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

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

El profesor se sorprenderá mucho al ver tu solución correcta😉

⌨

    Solución

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