1. The problem statement, all variables and given/known data (a)Let H and K be subgroups of a group G. Prove that the intersection of xH and yK which are cosets of H and K is either empty or else is a coset of the subgroup H intersect K (b) Prove that if H and K have finite index in G then the intersection of H and K also has finite index. 2. Relevant equations 3. The attempt at a solution The intersection of xH and yK is a subgroup of both H and K, then how to continue?