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Lógica matemática/ ¬(xvyz)v(pq)

Expresión ¬(xvyz)v(pq)

El profesor se sorprenderá mucho al ver tu solución correcta😉

⌨

    Solución

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