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Lógica matemática/ ABCD+ABCD+ABCD+AB+CD

Expresión ABCD+ABCD+ABCD+AB+CD

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    Solución

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