 Solution

A collection of logical connectives is adequate, or has functional completeness, if every Boolean function of finitely many propositional variables can be expressed by a formula using those connectives and variables, with the usual convention for nullary truth constants stated if those are included.

An adequate example is $\boxed{\{\neg ,\to \}}$. An inadequate example is $\boxed{\{\to \}}$: formulas using logical implication alone preserve truth when every input is true, so cannot express negation. These examples concern truth functions, rather than mere syntactic formation of formulas.