Sr Examen
Expresión {(~p^q)v(pvq)}{p^[q^(~rv~p)]}^~q
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
p∧q∧(¬q)∧((¬p)∨(¬r))∧(p∨q∨(q∧(¬p)))
$$p \wedge q \wedge \neg q \wedge \left(\neg p \vee \neg r\right) \wedge \left(p \vee q \vee \left(q \wedge \neg p\right)\right)$$
Solución detallada
$$p \vee q \vee \left(q \wedge \neg p\right) = p \vee q$$
$$p \wedge q \wedge \neg q \wedge \left(\neg p \vee \neg r\right) \wedge \left(p \vee q \vee \left(q \wedge \neg p\right)\right) = \text{False}$$
$$p \wedge q \wedge \neg q \wedge \left(\neg p \vee \neg r\right) \wedge \left(p \vee q \vee \left(q \wedge \neg p\right)\right) = \text{False}$$
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 | 0 | +---+---+---+--------+ | 1 | 1 | 0 | 0 | +---+---+---+--------+ | 1 | 1 | 1 | 0 | +---+---+---+--------+