Example of set difference: A = {0, 01}, and B = {0, 11}. Then, A B = {01}.

Prove that regular languages are closed under the set difference operation. That is, if A and B are regular languages, then, A B is also a regular language.

Hint: One can prove the statement above by either (1) contradiction or (2) construction. For the proof, you may make use of the theorems that regular languages are closed under union, intersection, and complement (already discussed in class).