In the following exercise, use the Pumping Lemma or the closure properties of regular languages to prove that the corresponding language is not regular.

C = {0^m1ⁿ | m n} (Note: This is an example where the pumping lemma is difficult to use. It is much easier to use the closure properties of regular languages.)

If you use the closure properties for the exercise, you need to transform (using the operations of union, intersection, complementation, concatenation, and star) the language C into L₁, and then L₁ into L₂, and so on till you reach a language that you know already is not regular. This implies that the initial language C is also not regular.