I am looking at a "practice test" for a Theory of Computation class. It was a test in a previous year.
I am asked to prove that, given L1 and L2 are regular, the union and difference are both regular.
It seems to me that for the union, since all the members of each separate set are regular, and the union consists exactly of all those members, therefore the union is regular.
And since the difference (L1-L2) is just a subset of L1, it is also regular.
This seems awfully straightforward and skips a lot of process.
Is it correct or am I missing something?