Make sure you understand the formulation (statement) of the pumping lemma and can accurately reproduce it. No proof of this lemma is required though.

Using the pumping lemma, prove that the language {0ⁿ1ⁿ | n0} is not regular.

Using the pumping lemma, prove that the language {ww | w{0,1}^*} is not regular.

Using the pumping lemma, prove that the language {0^m1ⁿ | 0 is not regular.

Using the pumping lemma, prove that the language {0^m1ⁿ | 0 is not regular (hint: think of pumping out instead of pumping in).