1. for each case below, decide whether a given language is a cfl, and prove your answer by constructing a pda or using the pumping lemma. a. l = { x { a, b, c }* | na(x) < nb(x) and na(x) < nc(x) }, where ni(x) is the number of occurrences of symbol i in x. b. l = { xayb | x, y { a, b}* and |x| = |y| } c. l = { xcx | x { a, b}* } d. l = { x{ a, b, c}* | na(x) = min(nb(x), nc(x)) } e. l = { w | w { a, b, c }*, numc numa + numb } f. l = { 0i1j | 2j i 4j }

Write a program that reads a file consisting of students’ test scores in the range 0–200. it should then determine the number of students having scores in each of the following ranges: 0–24, 25–49, 50–74, 75–99, 100–124, 125–149, 150–174, and 175–200. output the score ranges and the number of students. (run your program with the following input data: 76, 89, 150, 135, 200, 76, 12, 100, 150, 28, 178, 189, 167, 200, 175, 150, 87, 99, 129, 149, 176, 200, 87, 35, 157, 189.)