If a is a symbol and s is a string, define #a(s) to be the number of occurrences of a in s. For example, #1(101100101) = 5. Define #a(s) inductively, and then prove by structural induction that for any strings s and t, #a(s· t) = #a(s) + #a(t).

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1. ask the user how many questions are in the quiz. 2. ask the user to enter the key (that is, the correct answers). there should be one answer for each question in the quiz, and each answer should be an integer. e. g., 34 7 13 100 81 3 9 10 321 12 might be the key for a 10-question quiz. you will need to store the key in an array. 3. ask the user to enter the answers for the quiz to be graded. there needs to be one answer for each question. note that these answers do not need to be stored; each answer can simply be compared to the key as it is entered. 4. when the user has entered all of the answers to be graded, print the number correct and the percent correct. 5. add a loop so that the user can grade any number of quizzes with a single key. after the results have been printed for each quiz, ask "grade another quiz? (y/n)." note: you only have one array (the key). you are not creating a new key for each set of quiz answers.

Johnson enterprises uses a computer to handle its sales invoices. lately, business has been so good that it takes an extra 3 hours per night, plus every third saturday, to keep up with the volume of sales invoices. management is considering updating its computer with a faster model that would eliminate all of the overtime processing.