# The rank of the intersection of subgroups of a free group

Let $H$ and $K$ be finitely generated subgroups of a free group $F$, and suppose that $H$ has finite index in $F$. Is it true that $rank(H \cap K)-1 \leq (rank(H)-1)(rank(K)-1)$?

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(actually, I missed the "finite-index" part, so ignore my deleted comment). –  Andy Putman Nov 3 '13 at 19:32
@mary seva, it looks like your question is about to be closed (and/or migrated) as 'not research level'. In fact, I think it is graduate-student level, and hence acceptable on MO. But I suspect the formulation, which reads like a homework problem, has irritated the voters to close. Could you tell us how this problem arises in your research? –  HJRW Nov 3 '13 at 19:39
While this is certainly not a great question, why does it get THAT many downvotes? –  Stefan Kohl Nov 3 '13 at 19:50
@StefanKohl I am guessing because it looks like homework. –  Igor Rivin Nov 3 '13 at 20:00