Let G be a group. For any subsets H, K ⊆ G, define HK = {hk | h ∈ H, k ∈ K}, which is clearly a subset of G. If (ab)2=a2b2 for all a, b ∈ G, show G is abelian. If G is abelian, H ≤ G and K ≤ G (fixed subgroups), show HK G. True or false: If H ≤ G and K ≤ G (But without the assumption that G is abelian), then HK G. Give proof or a counterexample.