Respuesta :
Step-by-step explanation:
Consider the provided information.
We have given that H and k are the subgroups of orders 5 and 8, respectively.
We need to prove that H∩K = {e}.
As we know "Order of element divides order of group"
Here, the order of each element of H must divide 5 and every group has 1 identity element of order 1.
1 and 5 are the possible order of 5 order subgroup.
For subgroup order 8: The possible orders are 1, 2, 4 and 8.
Now we want to find the intersection of these two subgroups.
Clearly both subgroup H and k has only identity element in common.
Thus, H∩K = {e}.
