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Lógica matemática/ (a&c)v(b&d)(avb)&(c&d)

Expresión (a&c)v(b&d)(avb)&(c&d)

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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