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