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Lógica matemática/ (p∧q)∨(~p∧q∧r)

Expresión (p∧q)∨(~p∧q∧r)

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    Solución

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