I've come across that question : "Give examples of two regular languages which their union doesn't output a regular language. "
This is pretty shocking to me because I believe that regular languages are closed under union. Which means to me that if I take two regular languages and union them, I must get a regular language.
And I think I understand the proof of that : In my words, if the languages are regular, then there exist automatas that recognize them. If we take all the states (union), and we add a new state for the entry point, and we modify the transition function for the new state with epsilon, we are ok. We also show that there exist a path from every state etc.
Can you tell me where I'm wrong, or maybe another way to approach the question.
Source of the question, exercise 4, in french.
Also, the same question is asked with the intersection.