Formally prove the correctness of the union construction as follows. Let M1 and M2 be the two -NFA's constructed for R1 and R2 and let N be the -NFA constructed so that L(N) = R1 + R2. Let w be a string such that . Prove that either or . Use induction on all strings w.
Not only do I have no idea what to do, I don't even know what this is asking. Any push in the right direction would be helpful.