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Lógica matemática/ (P∧(Q∨R))∨(((P∧Q)∨R)∧P)

Expresión (P∧(Q∨R))∨(((P∧Q)∨R)∧P)

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    Solución

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