1. The problem statement, all variables and given/known data Let G be a group with subgroups H and K. Prove HintersectK is a subgroup. 2. Relevant equations 3. The attempt at a solution G is a group with subgroups H and K. Then H and K are closed, have identity elements in G and have inverses. HintersectK is a subgroup because H and K must satisfy the same properties of G.