Not a logical formula. The string has one opening parenthesis and no closing parenthesis, contradicting the parentheses count established above. It also fails the binary logical implication formation rule, whose final symbol must be a closing parenthesis.
Not a logical formula of this language. Logical disjunction is not one of its permitted logical connectives. Even though the displayed expression has an ordinary interpretation in a larger propositional language, membership in the specified formal language is a syntactic question. A logically equivalent logical formula using only negation and logical implication would have to be written with those symbols instead.
A logical formula. Both and are propositional variables, so and are logical formulas. Applying the binary logical implication formation rule to this ordered pair of logical formulas gives the displayed whole expression. This supplies a construction of its formula syntax tree rather than merely checking that its parentheses balance.

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