Expresión ((P→Q)∧(Q→P))↔(P↔Q)
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Solución detallada
$$p ⇔ q = \left(p \wedge q\right) \vee \left(\neg p \wedge \neg q\right)$$
$$p \Rightarrow q = q \vee \neg p$$
$$q \Rightarrow p = p \vee \neg q$$
$$\left(p \Rightarrow q\right) \wedge \left(q \Rightarrow p\right) = \left(p \wedge q\right) \vee \left(\neg p \wedge \neg q\right)$$
$$\left(\left(p \Rightarrow q\right) \wedge \left(q \Rightarrow p\right)\right) ⇔ \left(p ⇔ q\right) = 1$$
Tabla de verdad
+---+---+--------+
| p | q | result |
+===+===+========+
| 0 | 0 | 1 |
+---+---+--------+
| 0 | 1 | 1 |
+---+---+--------+
| 1 | 0 | 1 |
+---+---+--------+
| 1 | 1 | 1 |
+---+---+--------+