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.
Also, the same question is asked with the intersection.