The intersection of two subgroups of a group is always a:a.Subgroupb.Supergroupc.Cosetd.Non-group

To determine the intersection of two subgroups of a group, we need to follow these steps:

1. Identify the two subgroups of the given group.
2. Find the elements that are common to both subgroups.
3. Collect these common elements to form a new set.
4. Check if this new set satisfies the four conditions to be a subgroup: a. Closure: For any two elements in the set, their product or composition must also be in the set. b. Identity: The set must contain the identity element of the group. c. Inverses: For every element in the set, its inverse must also be in the set. d. Associativity: The operation defined on the group must be associative.

If the new set satisfies all four conditions, then it is the intersection of the two subgroups and it is also a subgroup of the given group. Therefore, the answer is (a) Subgroup.