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Lógica matemática/ abvyzvxz

Expresión abvyzvxz

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    Solución

    Ha introducido [src] 
    (a∧b)∨(x∧z)∨(y∧z)
    $$\left(a \wedge b\right) \vee \left(x \wedge z\right) \vee \left(y \wedge z\right)$$
    Simplificación [src]
    $$\left(a \wedge b\right) \vee \left(x \wedge z\right) \vee \left(y \wedge z\right)$$ 
    (a∧b)∨(x∧z)∨(y∧z)
    Tabla de verdad 
    +---+---+---+---+---+--------+
| a | b | x | y | z | result |
+===+===+===+===+===+========+
| 0 | 0 | 0 | 0 | 0 | 0      |
+---+---+---+---+---+--------+
| 0 | 0 | 0 | 0 | 1 | 0      |
+---+---+---+---+---+--------+
| 0 | 0 | 0 | 1 | 0 | 0      |
+---+---+---+---+---+--------+
| 0 | 0 | 0 | 1 | 1 | 1      |
+---+---+---+---+---+--------+
| 0 | 0 | 1 | 0 | 0 | 0      |
+---+---+---+---+---+--------+
| 0 | 0 | 1 | 0 | 1 | 1      |
+---+---+---+---+---+--------+
| 0 | 0 | 1 | 1 | 0 | 0      |
+---+---+---+---+---+--------+
| 0 | 0 | 1 | 1 | 1 | 1      |
+---+---+---+---+---+--------+
| 0 | 1 | 0 | 0 | 0 | 0      |
+---+---+---+---+---+--------+
| 0 | 1 | 0 | 0 | 1 | 0      |
+---+---+---+---+---+--------+
| 0 | 1 | 0 | 1 | 0 | 0      |
+---+---+---+---+---+--------+
| 0 | 1 | 0 | 1 | 1 | 1      |
+---+---+---+---+---+--------+
| 0 | 1 | 1 | 0 | 0 | 0      |
+---+---+---+---+---+--------+
| 0 | 1 | 1 | 0 | 1 | 1      |
+---+---+---+---+---+--------+
| 0 | 1 | 1 | 1 | 0 | 0      |
+---+---+---+---+---+--------+
| 0 | 1 | 1 | 1 | 1 | 1      |
+---+---+---+---+---+--------+
| 1 | 0 | 0 | 0 | 0 | 0      |
+---+---+---+---+---+--------+
| 1 | 0 | 0 | 0 | 1 | 0      |
+---+---+---+---+---+--------+
| 1 | 0 | 0 | 1 | 0 | 0      |
+---+---+---+---+---+--------+
| 1 | 0 | 0 | 1 | 1 | 1      |
+---+---+---+---+---+--------+
| 1 | 0 | 1 | 0 | 0 | 0      |
+---+---+---+---+---+--------+
| 1 | 0 | 1 | 0 | 1 | 1      |
+---+---+---+---+---+--------+
| 1 | 0 | 1 | 1 | 0 | 0      |
+---+---+---+---+---+--------+
| 1 | 0 | 1 | 1 | 1 | 1      |
+---+---+---+---+---+--------+
| 1 | 1 | 0 | 0 | 0 | 1      |
+---+---+---+---+---+--------+
| 1 | 1 | 0 | 0 | 1 | 1      |
+---+---+---+---+---+--------+
| 1 | 1 | 0 | 1 | 0 | 1      |
+---+---+---+---+---+--------+
| 1 | 1 | 0 | 1 | 1 | 1      |
+---+---+---+---+---+--------+
| 1 | 1 | 1 | 0 | 0 | 1      |
+---+---+---+---+---+--------+
| 1 | 1 | 1 | 0 | 1 | 1      |
+---+---+---+---+---+--------+
| 1 | 1 | 1 | 1 | 0 | 1      |
+---+---+---+---+---+--------+
| 1 | 1 | 1 | 1 | 1 | 1      |
+---+---+---+---+---+--------+
    FNCD [src]
    $$\left(a \vee z\right) \wedge \left(b \vee z\right) \wedge \left(a \vee x \vee y\right) \wedge \left(b \vee x \vee y\right)$$ 
    (a∨z)∧(b∨z)∧(a∨x∨y)∧(b∨x∨y)
    FNDP [src]
    $$\left(a \wedge b\right) \vee \left(x \wedge z\right) \vee \left(y \wedge z\right)$$ 
    (a∧b)∨(x∧z)∨(y∧z)
    FNC [src]
    $$\left(a \vee z\right) \wedge \left(b \vee z\right) \wedge \left(a \vee x \vee y\right) \wedge \left(a \vee x \vee z\right) \wedge \left(a \vee y \vee z\right) \wedge \left(b \vee x \vee y\right) \wedge \left(b \vee x \vee z\right) \wedge \left(b \vee y \vee z\right)$$ 
    (a∨z)∧(b∨z)∧(a∨x∨y)∧(a∨x∨z)∧(a∨y∨z)∧(b∨x∨y)∧(b∨x∨z)∧(b∨y∨z)
    FND [src]
    Ya está reducido a FND
    $$\left(a \wedge b\right) \vee \left(x \wedge z\right) \vee \left(y \wedge z\right)$$ 
    (a∧b)∨(x∧z)∨(y∧z)
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