1. The problem statement, all variables and given/known data Let G be a group, and let H and K be two subgroups of G. Then the union of H and K is a subgroup of G such that the intersection of H and K is an empty set. Can you visualize the product hk in a venn diagram for all h which belongs to H and for all k which belongs to K? 3. The attempt at a solution You cannot because: Take a point h at the top of H group where derivate of the "circle" is zero. Take similarly a point k at the top of K. Let k=(-1, 10) and h=(1, 10). The product kh is 10 * 10 = 100 in y-direction, while -1 * 1 = -1 in x-direction. Thus, we get a point kh = (-1,100) which does NOT belong to H nor K. This suggests me that the set of the union H and K is greater than than the high-school presentation of the union. It seems that we cannot use venn diagrams in such problems.