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Lógica matemática/ pv(r&!r)v(q&r)v(!p&q&r)

Expresión pv(r&!r)v(q&r)v(!p&q&r)

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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