# 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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#### Solution Preview

Proof:

"<=": If H ⊆ K, then H∪K=K. Since K is a subgroup of G, then H∪K is a subgroup of G.

If K ⊆ H, then H∪K=H. Since H is a subgroup of G, then H∪K is a ...

#### Solution Summary

Groups and subgroups are investigated.

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