Problem 5.5.1 if l is a language and a is a letter, we define the quotient of l by a, written la−1 , as follows. la−1 consists of all those strings that would be in l if you appended an a to them – formally, la−1 = {w : wa ∈ l}. prove that if s is any regular expression, and a is any letter, then l(s)a −1 is a regular language. give a recursive algorithm to produce a regular expression for this language.