1- For a word w, the reverse of w is the word in which the characters of w appear in the reverse order. Let w^R denote the reverse of w. For a language L, define L^R to be the language of all w such that w^R is in L. Prove that, if L is regular, then L^R is regular. This can be accomplished by showing that there is an NFA for L^R.

2- Let B be regular. Define C = {uvw | u,v,w and v B}. Show that C is regular.

3- Suppose both A and B are regular. Define L = {w | w A and w does not contain a substring that is a member of B}. Prove that L is regular.