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