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Lógica matemática/ not((zvp&q)¬(x&y))

Expresión not((zvp&q)¬(x&y))

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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