= Solution
Use <structural induction> on the formation of a <propositional formula>. A <propositional variable> has no parentheses. Applying <negation> to a <logical formula> adds no parentheses, so preserves <equality> of the two counts. If $\psi$ and $\chi$ each have equally many opening and closing parentheses, the formation of $(\psi\to\chi)$ adds one of each to their combined counts. Thus every <propositional formula> satisfies
$$
\boxed{\#\text{ opening parentheses}=\#\text{ closing parentheses}.}
$$
This is a necessary condition for being a <logical formula>; it is not sufficient, since the <logical connectives> and the placement of symbols must also follow the <formation rules>.
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