hho be means of examples that union of t o subgroups may or may not be subgroups.

It seems like your question is about demonstrating through examples that the union of two subgroups may or may not be a subgroup. Here are two examples:

1. Union of Two Subgroups is Not a Subgroup:

Consider two subgroups H and K of a group G. Let's say H = {e, a} and K = {e, b} where e is the identity, a and b are elements of G. The union of H and K is {e, a, b}. This set is not a subgroup of G because it's not closed under the operation of the group. For instance, if the operation is , then ab is not in {e, a, b}.

2. Union of Two Subgroups is a Subgroup:

Consider two subgroups H and K of a group G such that H is contained in K. In this case, the union of H and K is just K, which is a subgroup of G. For example, let's say H = {e} and K = {e, a, b}. The union of H and K is {e, a, b}, which is a subgroup of G.

So, the union of two subgroups may or may not be a subgroup depending on the specific subgroups and the operation of the group.