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.

Amajor grocery store chain is trying to cut down on waste. currently, they get peaches from two different distributors, whole fruits and green grocer. out of a two large shipments, the manager randomly selects items from both suppliers and counts the number of items that are not sell-able due to bruising, disease or other problems. she then makes a confidence interval. is there a significant difference in the quality of the peaches between the two distributors? 95% ci for pw-pg: (0.064, 0.156)