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∧(((¬p)∨(¬q))⇒(r∧s∧(¬t)∧(r⇒t)))
$$p \wedge \left(\left(\neg p \vee \neg q\right) \Rightarrow \left(r \wedge s \wedge \left(r \Rightarrow t\right) \wedge \neg t\right)\right)$$
Solución detallada
$$r \Rightarrow t = t \vee \neg r$$
$$r \wedge s \wedge \left(r \Rightarrow t\right) \wedge \neg t = \text{False}$$
$$\left(\neg p \vee \neg q\right) \Rightarrow \left(r \wedge s \wedge \left(r \Rightarrow t\right) \wedge \neg t\right) = p \wedge q$$
$$p \wedge \left(\left(\neg p \vee \neg q\right) \Rightarrow \left(r \wedge s \wedge \left(r \Rightarrow t\right) \wedge \neg t\right)\right) = p \wedge q$$
$$r \wedge s \wedge \left(r \Rightarrow t\right) \wedge \neg t = \text{False}$$
$$\left(\neg p \vee \neg q\right) \Rightarrow \left(r \wedge s \wedge \left(r \Rightarrow t\right) \wedge \neg t\right) = p \wedge q$$
$$p \wedge \left(\left(\neg p \vee \neg q\right) \Rightarrow \left(r \wedge s \wedge \left(r \Rightarrow t\right) \wedge \neg t\right)\right) = p \wedge q$$
Tabla de verdad
+---+---+---+---+---+--------+ | p | q | r | s | t | result | +===+===+===+===+===+========+ | 0 | 0 | 0 | 0 | 0 | 0 | +---+---+---+---+---+--------+ | 0 | 0 | 0 | 0 | 1 | 0 | +---+---+---+---+---+--------+ | 0 | 0 | 0 | 1 | 0 | 0 | +---+---+---+---+---+--------+ | 0 | 0 | 0 | 1 | 1 | 0 | +---+---+---+---+---+--------+ | 0 | 0 | 1 | 0 | 0 | 0 | +---+---+---+---+---+--------+ | 0 | 0 | 1 | 0 | 1 | 0 | +---+---+---+---+---+--------+ | 0 | 0 | 1 | 1 | 0 | 0 | +---+---+---+---+---+--------+ | 0 | 0 | 1 | 1 | 1 | 0 | +---+---+---+---+---+--------+ | 0 | 1 | 0 | 0 | 0 | 0 | +---+---+---+---+---+--------+ | 0 | 1 | 0 | 0 | 1 | 0 | +---+---+---+---+---+--------+ | 0 | 1 | 0 | 1 | 0 | 0 | +---+---+---+---+---+--------+ | 0 | 1 | 0 | 1 | 1 | 0 | +---+---+---+---+---+--------+ | 0 | 1 | 1 | 0 | 0 | 0 | +---+---+---+---+---+--------+ | 0 | 1 | 1 | 0 | 1 | 0 | +---+---+---+---+---+--------+ | 0 | 1 | 1 | 1 | 0 | 0 | +---+---+---+---+---+--------+ | 0 | 1 | 1 | 1 | 1 | 0 | +---+---+---+---+---+--------+ | 1 | 0 | 0 | 0 | 0 | 0 | +---+---+---+---+---+--------+ | 1 | 0 | 0 | 0 | 1 | 0 | +---+---+---+---+---+--------+ | 1 | 0 | 0 | 1 | 0 | 0 | +---+---+---+---+---+--------+ | 1 | 0 | 0 | 1 | 1 | 0 | +---+---+---+---+---+--------+ | 1 | 0 | 1 | 0 | 0 | 0 | +---+---+---+---+---+--------+ | 1 | 0 | 1 | 0 | 1 | 0 | +---+---+---+---+---+--------+ | 1 | 0 | 1 | 1 | 0 | 0 | +---+---+---+---+---+--------+ | 1 | 0 | 1 | 1 | 1 | 0 | +---+---+---+---+---+--------+ | 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 | +---+---+---+---+---+--------+