There is a regular language insert1(L) := {x1y | x y L} . Intuitively, insert1(L) is the set of all strings that can be obtained from strings in L by inserting exactly one 1. For example, if L = {",OOK!}, then insert1(L) = {1,1OOK!,O1OK!, OO1K!,OOK1!,OOK!1}.

1. Suppose r1 and r2 are regular expressions, and r'1 and r'2 are regular expressions for the languages insert1(L(r1 )) and insert1(L(r2 )) respectively. Describe a regular expression for the language insert1(L(r1 + r2 )) using r1 ,r2 ,r'1 ,r'2 .

2. Same as the previous part but now consider L(r1 r2 ).

3. Same as the previous part but now consider L((r1)*).