Similar question has been asked on SE before but the problem statement is usually more specific and gives more information (in particular, tells you what to prove), but this problem asks to prove or disprove: For a group $G$ and subgroups $H$ and $K$, if $|G:H|$ and $|G:K|$ are finite then so is $|G:H \cap K|$.
Is there an easy way to see this is true with given just statement?