For each re, state which of the following strings is in the language of the re: ε, abba, bababb, and b.

a) (a+b)*ab(a+b)*

b) b* ab*ab*

c) a+(a*b)*

for each re, give two strings that are in ther corresponding language and two strings that are not:

a)a(a+b)*b

b)a*a+ε+b*

c) (ab+ba)*

Jason, samantha, ravi, sheila, and ankit are preparing for an upcoming marathon. each day of the week, they run a certain number of miles and write them into a notebook. at the end of the week, they would like to know the number of miles run each day, the total miles for the week, and average miles run each day. write a program to them analyze their data. your program must contain parallel arrays: an array to store the names of the runners and a two-dimensional array of five rows and seven columns to store the number of miles run by each runner each day. furthermore, your program must contain at least the following functions: a function to read and store the runners’ names and the numbers of miles run each day; a function to find the total miles run by each runner and the average number of miles run each day; and a function to output the results. (you may assume that the input data is stored in a file and each line of data is in the following form: runnername milesday1 milesday2 milesday3 milesday4 milesday5 milesday6 milesday7.)