# Union subgroup implies that the group is one of the subgroups. [duplicate]

Suppose $G$ is a group and $H_1, H_2\leq G$ such that $H_1\cup H_2=G.$

How can I prove that either $G=H_1$ or $G=H_2$?

• Suppose both were proper subgroups. Choose $g_i \in G\setminus H_i$, then ... Feb 22, 2014 at 0:03
• I'm confused - such that $H_1\cup H_2$ what?
– user122283
Feb 22, 2014 at 0:05
• Prove that $H_1 \cup H_2$ is a subgroup of $G$ if and only if $H_1 \subset H_2$ or $H_2 \subset H_1$ Feb 22, 2014 at 0:10