Plz help me to solve this question​

Show that there is a language a ⚆ {0, 1} â— with the following properties: 1. for all x â a, |x| ≤ 5. 2. no dfa with fewer than 9 states recognizes a. hint: you don’t have to define a explicitly; just show that it has to exist. count the number of languages satisfying (1) and the number of dfas satisfying (2), and argue that there aren’t enough dfas to recognize all those languages. to count the number of languages satisfying (1), think about writing down all the strings of length at most 5, and then to define such a language, you have to make a binary decision for each string about whether to include it in the language or not. how many ways are there to make these choices? to count the number of dfas satisfying (2), consider that a dfa behaves identically even if you rename all the states, so you can assume without loss of generality that any dfa with k states has the state set {q1, q2, . . , qk}. now think about how to count how many ways there are to choose the other four parts of the dfa.

1)consider the following code snippet: #ifndef book_h#define book_hconst double max_cost = 1000.0; class book{public: book(); book(double new_cost); void set_cost(double new_cost); double get_cost() const; private: double cost; }; double calculate_terms(book bk); #endifwhich of the following is correct? a)the header file is correct as given. b)the definition of max_cost should be removed since header files should not contain constants. c)the definition of book should be removed since header files should not contain class definitions. d)the body of the calculate_terms function should be added to the header file.

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.)