Show that a group can not be expressed as union of two of its proper subgroups [duplicate]

Show that a group can not be expressed as union of two of its proper subgroups. I am not sure how to start.

HINT: Suppose that $H,K<G$, and let $h\in H\setminus K$ and $k\in K\setminus H$; where is $hk$?

• I was just about to ask how to continue and I got it :) (+1) Sep 4, 2013 at 20:01