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Lógica matemática/ f(x1,x2,x3)=x1*x2∨x3>x1*x3

Expresión f(x1,x2,x3)=x1*x2∨x3>x1*x3

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    Solución

    Ha introducido [src] 
    (x3∨(x1∧x2))⇒(x1∧x3)
    $$\left(x_{3} \vee \left(x_{1} \wedge x_{2}\right)\right) \Rightarrow \left(x_{1} \wedge x_{3}\right)$$
    Solución detallada
    $$\left(x_{3} \vee \left(x_{1} \wedge x_{2}\right)\right) \Rightarrow \left(x_{1} \wedge x_{3}\right) = \left(x_{1} \wedge x_{3}\right) \vee \left(\neg x_{1} \wedge \neg x_{3}\right) \vee \left(\neg x_{2} \wedge \neg x_{3}\right)$$
    Simplificación [src]
    $$\left(x_{1} \wedge x_{3}\right) \vee \left(\neg x_{1} \wedge \neg x_{3}\right) \vee \left(\neg x_{2} \wedge \neg x_{3}\right)$$ 
    (x1∧x3)∨((¬x1)∧(¬x3))∨((¬x2)∧(¬x3))
    Tabla de verdad 
    +----+----+----+--------+
| x1 | x2 | x3 | result |
+====+====+====+========+
| 0  | 0  | 0  | 1      |
+----+----+----+--------+
| 0  | 0  | 1  | 0      |
+----+----+----+--------+
| 0  | 1  | 0  | 1      |
+----+----+----+--------+
| 0  | 1  | 1  | 0      |
+----+----+----+--------+
| 1  | 0  | 0  | 1      |
+----+----+----+--------+
| 1  | 0  | 1  | 1      |
+----+----+----+--------+
| 1  | 1  | 0  | 0      |
+----+----+----+--------+
| 1  | 1  | 1  | 1      |
+----+----+----+--------+
    FNC [src]
    $$\left(x_{1} \vee \neg x_{3}\right) \wedge \left(x_{3} \vee \neg x_{3}\right) \wedge \left(x_{1} \vee \neg x_{1} \vee \neg x_{2}\right) \wedge \left(x_{1} \vee \neg x_{1} \vee \neg x_{3}\right) \wedge \left(x_{1} \vee \neg x_{2} \vee \neg x_{3}\right) \wedge \left(x_{3} \vee \neg x_{1} \vee \neg x_{2}\right) \wedge \left(x_{3} \vee \neg x_{1} \vee \neg x_{3}\right) \wedge \left(x_{3} \vee \neg x_{2} \vee \neg x_{3}\right)$$ 
    (x1∨(¬x3))∧(x3∨(¬x3))∧(x1∨(¬x1)∨(¬x2))∧(x1∨(¬x1)∨(¬x3))∧(x1∨(¬x2)∨(¬x3))∧(x3∨(¬x1)∨(¬x2))∧(x3∨(¬x1)∨(¬x3))∧(x3∨(¬x2)∨(¬x3))
    FNDP [src]
    $$\left(x_{1} \wedge x_{3}\right) \vee \left(\neg x_{1} \wedge \neg x_{3}\right) \vee \left(\neg x_{2} \wedge \neg x_{3}\right)$$ 
    (x1∧x3)∨((¬x1)∧(¬x3))∨((¬x2)∧(¬x3))
    FND [src]
    Ya está reducido a FND
    $$\left(x_{1} \wedge x_{3}\right) \vee \left(\neg x_{1} \wedge \neg x_{3}\right) \vee \left(\neg x_{2} \wedge \neg x_{3}\right)$$ 
    (x1∧x3)∨((¬x1)∧(¬x3))∨((¬x2)∧(¬x3))
    FNCD [src]
    $$\left(x_{1} \vee \neg x_{3}\right) \wedge \left(x_{3} \vee \neg x_{1} \vee \neg x_{2}\right)$$ 
    (x1∨(¬x3))∧(x3∨(¬x1)∨(¬x2))
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