Sr Examen
Expresión (¬PVQ)∧¬(¬(R→¬Q)V¬R)
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
(q∨(¬p))∧(¬((¬r)∨(¬(r⇒(¬q)))))
$$\neg \left(\neg r \vee r \not\Rightarrow \neg q\right) \wedge \left(q \vee \neg p\right)$$
Solución detallada
$$r \Rightarrow \neg q = \neg q \vee \neg r$$
$$r \not\Rightarrow \neg q = q \wedge r$$
$$\neg r \vee r \not\Rightarrow \neg q = q \vee \neg r$$
$$\neg \left(\neg r \vee r \not\Rightarrow \neg q\right) = r \wedge \neg q$$
$$\neg \left(\neg r \vee r \not\Rightarrow \neg q\right) \wedge \left(q \vee \neg p\right) = r \wedge \neg p \wedge \neg q$$
$$r \not\Rightarrow \neg q = q \wedge r$$
$$\neg r \vee r \not\Rightarrow \neg q = q \vee \neg r$$
$$\neg \left(\neg r \vee r \not\Rightarrow \neg q\right) = r \wedge \neg q$$
$$\neg \left(\neg r \vee r \not\Rightarrow \neg q\right) \wedge \left(q \vee \neg p\right) = r \wedge \neg p \wedge \neg q$$
Tabla de verdad
+---+---+---+--------+ | p | q | r | result | +===+===+===+========+ | 0 | 0 | 0 | 0 | +---+---+---+--------+ | 0 | 0 | 1 | 1 | +---+---+---+--------+ | 0 | 1 | 0 | 0 | +---+---+---+--------+ | 0 | 1 | 1 | 0 | +---+---+---+--------+ | 1 | 0 | 0 | 0 | +---+---+---+--------+ | 1 | 0 | 1 | 0 | +---+---+---+--------+ | 1 | 1 | 0 | 0 | +---+---+---+--------+ | 1 | 1 | 1 | 0 | +---+---+---+--------+