# Math Help - subgroup/group theory

1. ## subgroup/group theory

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!

2. hi--

i give u a hint

there will be 2 parts to this question.

Assume: $H \cup K$ is a subgroup. Think what happens when H is not contained in K or vice versa.

Converse: this is very easy. Take $x,y \in H$ or $K$. Since $H,K$ are subgroups the statement follows