Question

Give an example of two languages L1 and L2 satisfying the following conditions at the same time.

1. L1 is a non-regular language;
2. L2 is a regular language;
3. L1 ⊂ L2.

Answer 1

L1={aⁿbⁿ | n>0 alphabet={a,b}}

L1={ab,aabb,aaabbb,....}

L2={(a+b)*| alphabet={a,b}}

L2={e,a,b,ab,aa,ba,bb,.......,aabb,..,aaabbb,.....}

L2 is the set of all strings over a,b including (a,b).

Whereas L1 contains strings ove a,b where any string does not contain substring ' ba ' and does not contain e.