### Homework #6 Results and Key

Mean: 82.4%; standard deviation: 21.9%

Most did quite well. Scaffolding provided by the textbook was no doubt a factor.

Many points were lost when folks did not follow instructions. If asked to use the Pumping Lemma, use the Pumping Lemma. If asked to use Theorem 11.1, use Theorem 11.1.

Please write complete proofs. Convincing your grader that you understand how the Pumping Lemma works is one thing. Convincing your grader that you can write a proof that will convince someone else that the language {$a^n b^n c^n$} is not regular is quite a different thing. You need to do both.

A professor once told me: “When you write a proof, you must touch my heart. You must make me believe. You must make me believe in my heart that it is true.” Guess which professor this was. You have one guess.