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    Groups and Subgroups

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    Let G be a group and let H and K be subgroups of G. Prove that H∪K is a subgroup of G if and only if H ⊆ K or K ⊆ H.

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    "<=": If H &#8838; K, then H&#8746;K=K. Since K is a subgroup of G, then H&#8746;K is a subgroup of G.
    If K &#8838; H, then H&#8746;K=H. Since H is a subgroup of G, then H&#8746;K is a ...

    Solution Summary

    Groups and subgroups are investigated.