Sr Examen
Lógica matemática/ not(xnotq(y+zp))

Expresión not(xnotq(y+zp))

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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