let H and K be subgroups of G. Prove that H U K is a subgroup iff either H is a subset of K or K is a subset of H?
just having trouble with this problem. appreciate a few pointers.
Thank you!
hi--
i give u a hint
there will be 2 parts to this question.
Assume: $\displaystyle H \cup K$ is a subgroup. Think what happens when H is not contained in K or vice versa.
Converse: this is very easy. Take $\displaystyle x,y \in H$ or $\displaystyle K$. Since $\displaystyle H,K$ are subgroups the statement follows