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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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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