Find two sets S and T so that S union T is regular but S is

Find two sets S and T so that S union T is regular but S is not.

Solution

A regular set can be defined as- T= {, a, aaa, aaaaa,.....} String of odd lenght.

A non regular set can be defined as S={ab,aabb,aaabbb,...} here there are as many a as the number of b.

Now we know that Union of  regular language and an irregular language is regular language,

Hence,

T U S = T, which is regular.

{,a,ab,aaa,aabb,aaaaa,aaabbb,.......}