Let L be the set of exactly those strings over the alphabet \Sigma = {a, b, c, g}, that satisfy all of the following properties: the length of the string is equal to 5n+3, for some natural number n greater or equal than 0; all of the first (leftmost) 2n symbols are elements of the set {b, c, g}; all of the last (rightmost) 3n symbols are elements of the set {a, b}; the symbols at position 2n+1, 2n+2, and 2n+3 (from the left, i. e., after the first 2n symbols but before the last 3n symbols) are elements of the set {c, g}; Write a complete formal definition of a context free grammar that generates L. If such a context free grammar does not exist, state that the context free grammar does not exist, and prove it.

Multiple choice project create a program with two multiple choice questions. 1. users have two attempts only, show attempt number each time. hint: while loop with break control. (20%) 2. only one correct answer for each question, use switch case for each question. (20%) 3. show total score after the two questions are answered. hint: . (20%) 4. user have options to answer the two questions again if first attempt score is not 100%. hint: if statment. (20%) 5. use string method .toupper() to allow users to enter with lowercase or uppercase letters. (20%) 1. where is the capital of the state of florida? a. orlando b. tallahassee c. miami d. tampa b 2. where is walt disney world park located in florida? a. orlando b. tallahassee c. miami d. tampa a