Is every subset of the regular language is regular, and why?

Question

Is every subset of the regular language is regular, and why?

Answer 1

A subset of a regular language might not be regular.

Example:

L1 = {(a^m)(b^n)}, m >= 0, n >= 0

L2 = {(a^m)(b^m)}, m >= 0

L1 is regular. L2 is a subset of L1, but L2 is not regular.