need help with q8 ?

a) Construct a regular grammar from M that generates LOM) b) Give a regular expression for L(M). 6. Le t G be a regular grammar and M the NFA obtained from G rem 6.3.1. Prove that if S 15. Prove t 16. Let L b wC, then there is a computation (S, w]IC. Alin to t L be a regular language over (a, b, c). Show that each of the following eu regular. (w we L and w ends with aa) b) (wl w e L or w contains an a) c) furt to L and w does not contain an a} 17. Let L Prove that the family of regular languages is closed under the operation of set differenc 18. Gi 9 Prove that the family ofregular languages is not closed under intersection with com free languages. That is, if L is regular and L, context-free, LnLi need not be regulaz 10. Is the family of regular languages closed under infinite unions? That is, if Lg.LiL. are regular, is UL, necessarily regular? If so, prove it:If not, give a counterexample 11. Let L be a regular language. Show that the following languages are regular. a) The set P = { u u E L} of prefixes of strings in L. b) The set LR (wRwELj of reversals of strings in L. c) The set E = (u I u E L) of strings that have a suffix in L. d) The set SUR = (u I MUUE LI of strings that are substrin ng in L