Let and be subgroups of the group , and let . Show that either or else is a left coset of .
I've been working on this one for over a day, now, and I'm still stumped. Assistance would therefore be much appreciated!
EDIT: I finally solved it, and it is indeed extremely simple. I can't believe I missed it for so long.
Proof: Suppose , and let . Then there are , with . So , and therefore . The conclusion follows.