I want the answers for 10 27 and 7

7. Construct a grammar over {a, b, c} whose language is {anb2nem I n, m > 0). 8. Construct a grammar over fa, b, c) whose language is la"b"c2*-m 9. Construct a grammar over la, b,cl whose languageis (a"b 0si Exercises 99 10. Construct a grammar over (a, b) whose language is (a"b" 10snm3n) 11. Construct a grammar over (a, b) whose language is (a"ba"mn). precede the c's. It is possible that there are no a's, b's, or c's. 16. The set of strings over fa, b) that contain the substring aa and the substring bb. 17. The set of strings over (a, b) in which the substring aa occurs at least twice. (Hint: Beware of the substring aaa.) 18. The set of strings over [a, b) that contain the substring ab and the substring ba. i 19. The set of strings over [a, b) in which the number of a's is divisible by three 20. The set of strings over (a, b) in which every a is either immediately preceded or immediately followed by b, for example, baab, aba, andb 21. The set of strings over [a, b) that do not contain the substring aba 22. The set of strings over (a, b] in which the substring aa occurs exactly once. 23. set of strings of odd length over {a, b} that contain exactly two b's 24. The set of strings over [a, b, c) with an odd number of occurrences of the substring 25. The set of strings over fa, b) with an even number of a's or an odd number of b's 26. The grammar in Figure 3.1 generates (b ab ab")+, the set of all strings with a positive, even number of a's. Prove this. 27. Prove that the grammar given in Example 3.2.2 generates the prescribed language. 28. Let G be the grammar B-bB b. Prove that L(G)- (a"b" I0n