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