2. Let H and K be subgroups of the group G. hyk for some h e H and k e K. Show that ~ is an (a) For x, y E G, define x ~ y if x = equivalence relation on G. (b) The equivalence class of x E G is HxK...

please just answer b

Extracted text: 2. Let H and K be subgroups of the group G. hyk for some h e H and k e K. Show that ~ is an (a) For x, y E G, define x ~ y if x = equivalence relation on G. (b) The equivalence class of x E G is HxK coset of H and K. Show that the double cosets of H and K partition G, and that each double coset is a union of right cosets of H and is a union of left cosets of K. {hxk | h e H, k e K}. It is called a double