Recall that two strings u and v are ANAGRAMS if the letters of one can be rearranged to form the other, or, equivalently, if they contain the same number of each letter. If L is a language, we define its ANAGRAM CLOSURE AC(L) to be the set of all strings that have an anagram in L. Prove that the set of regular languages is _not_ closed under this operation. That is, find a regular language L such that AC(L) is not regular. (We’re now allowed to use Kleene’s Theorem, so you just need to show that AC(L) is not recognizable.)
