Sr Examen
Expresión ¬(P∨¬(Q∧R))∨(¬(P∨Q)∧R)
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
(r∧(¬(p∨q)))∨(¬(p∨(¬(q∧r))))
$$\left(r \wedge \neg \left(p \vee q\right)\right) \vee \neg \left(p \vee \neg \left(q \wedge r\right)\right)$$
Solución detallada
$$\neg \left(p \vee q\right) = \neg p \wedge \neg q$$
$$r \wedge \neg \left(p \vee q\right) = r \wedge \neg p \wedge \neg q$$
$$\neg \left(q \wedge r\right) = \neg q \vee \neg r$$
$$p \vee \neg \left(q \wedge r\right) = p \vee \neg q \vee \neg r$$
$$\neg \left(p \vee \neg \left(q \wedge r\right)\right) = q \wedge r \wedge \neg p$$
$$\left(r \wedge \neg \left(p \vee q\right)\right) \vee \neg \left(p \vee \neg \left(q \wedge r\right)\right) = r \wedge \neg p$$
$$r \wedge \neg \left(p \vee q\right) = r \wedge \neg p \wedge \neg q$$
$$\neg \left(q \wedge r\right) = \neg q \vee \neg r$$
$$p \vee \neg \left(q \wedge r\right) = p \vee \neg q \vee \neg r$$
$$\neg \left(p \vee \neg \left(q \wedge r\right)\right) = q \wedge r \wedge \neg p$$
$$\left(r \wedge \neg \left(p \vee q\right)\right) \vee \neg \left(p \vee \neg \left(q \wedge r\right)\right) = r \wedge \neg p$$
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 | 0 | +---+---+---+--------+ | 1 | 1 | 0 | 0 | +---+---+---+--------+ | 1 | 1 | 1 | 0 | +---+---+---+--------+