Closure lab
The regular languages are closed under all of these, and each closure result is a construction rather than a fact to memorise. Pick one and watch it get built.
Hopcroft 2e §4.2. Union, intersection and difference share a single product walk and differ only in which pairs accept — worth noticing, since they are usually taught as three separate theorems.
A pair accepts when both do.
L₁
L₂
Result
Narration
Build the product of the two machines, starting at (q0,q0). A pair accepts when both machines accept.
The answer appears at the last step. if you would rather read it than watch it.