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Lógica matemática/ not(zvp&q)&(x&y)

Expresión not(zvp&q)&(x&y)

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    Solución

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