I need to prove or disprove with contrast example:
If $L_1$ and $L_2$ are non regular then $L_1 \cup\;L_2\; = L$ can be regular
I have no idea how to begin, hints and spoilers are welcomed
2026-03-29 19:11:17.1774811477
If $L_1$ and $L_2$ are non regular then $L_1 \cup\;L_2\; = L$ can be regular?
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How about $L_1=\{\mathtt a^n\mid n\text{ is prime}\}$ and $L_2=\{\mathtt a^n\mid n\text{ is composite}\}$?