Sr Examen
Lógica matemática/ ((pv~r)^~r)→(p^q)

Expresión ((pv~r)^~r)→(p^q)

El profesor se sorprenderá mucho al ver tu solución correcta😉

⌨

    Solución

    Ha introducido [src] 
    ((¬r)∧(p∨(¬r)))⇒(p∧q)
    $$\left(\neg r \wedge \left(p \vee \neg r\right)\right) \Rightarrow \left(p \wedge q\right)$$
    Solución detallada
    $$\neg r \wedge \left(p \vee \neg r\right) = \neg r$$
    $$\left(\neg r \wedge \left(p \vee \neg r\right)\right) \Rightarrow \left(p \wedge q\right) = r \vee \left(p \wedge q\right)$$
    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      |
+---+---+---+--------+
    FNCD [src]
    $$\left(p \vee r\right) \wedge \left(q \vee r\right)$$ 
    (p∨r)∧(q∨r)
    FNC [src]
    $$\left(p \vee r\right) \wedge \left(q \vee r\right)$$ 
    (p∨r)∧(q∨r)
    FND [src]
    Ya está reducido a FND
    $$r \vee \left(p \wedge q\right)$$ 
    r∨(p∧q)
    FNDP [src]
    $$r \vee \left(p \wedge q\right)$$ 
    r∨(p∧q)
    © Sr Examen