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Lógica matemática/ NOTY&NOTP&NOT(X&Z)

Expresión NOTY&NOTP&NOT(X&Z)

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    Solución

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