Prove two subgroups have the same order given an equivalence relation. Let $X$ be the set of all subgroups of a group $G$. The following is an equivalence relation $H$~$K$ where $H=xKx^{-1}$.
Prove: If $H$~$K$, then $|H|=|K|$.  
I'm guessing $H$,$K$ are subgroups of a group $G$.  Other than that, I'm not quite sure where to start on this one.  I know that if $|H|=|K|$ then they have the same amount of elements in them but I'm not sure how to prove that given the equivalence relation.

Alternatively check the inverse of the function $f(h)=ghg^{-1}$ is $g^{-1}hg. $ Hence $f$ is a bijection with the appropriate co-domain.
