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Lógica matemática/ xy∨yzt∨xyzt

Expresión xy∨yzt∨xyzt

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    Solución

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