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 $G=H_2$?
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Suppose both were proper subgroups. Choose $g_i \in G\setminus H_i$, then ... – Daniel Fischer Feb 22 '14 at 00:03
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I'm confused - such that $H_1\cup H_2$ what? – Feb 22 '14 at 00:05
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Prove that $H_1 \cup H_2$ is a subgroup of $G$ if and only if $H_1 \subset H_2$ or $H_2 \subset H_1$ – dani_s Feb 22 '14 at 00:10