Prove that language $|>$ mandk $\{$:$=n-m\}$ over alphabet $\{a,b,c\}$ is not regular. Make your proof clear and readable. Do not expect the reader to guess what you are doing. Do not use the Pumping Lemma. Follow this outline.

$($a$)$ The proof is by contradiction. Suppose that $A$ is regular. That means there is a DFA $M$ that solves $A.$ Do an experiment on $M$ by running it on a sequence of strings. What is the sequence of strings that you run $A$ on$?($Only say what the sequence of strings is here.$)$

$($b$)$ What can you conclude from the experiment in part $($a$)?$

$($c$)$ Using the information from part $($b$),$ show that $M$ does not solve $A.$ That contradicts the assumption that $M$ solves $A.$