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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$\begingroup$ Suppose both were proper subgroups. Choose $g_i \in G\setminus H_i$, then ... $\endgroup$– Daniel FischerFeb 22, 2014 at 0:03
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$\begingroup$ I'm confused - such that $H_1\cup H_2$ what? $\endgroup$– user122283Feb 22, 2014 at 0:05
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$\begingroup$ Prove that $H_1 \cup H_2$ is a subgroup of $G$ if and only if $H_1 \subset H_2$ or $H_2 \subset H_1$ $\endgroup$– dani_sFeb 22, 2014 at 0:10
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