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Lógica matemática/ {p∧[qv(~p)]}vr

Expresión {p∧[qv(~p)]}vr

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    Solución

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