Given a group $G$ and two subgroups $H_1\leq G$ and $H_2\leq G$.
Also: $H_1\cup H_2= G$.
I have to prove, that either $H_1=G$ or $H_2=G$.
So, if the group $G$ is the union of the two subgroups $H_1$ and $H_2$, I must prove, that either $H_1$ or $H_2$ are trivial groups, am I correct?
But how would I do that?