True or False:
If H and K are subgroups of G, then is a subgroup of G.
If is a subgroup of G for all , then is a subgroup of G.
Explanations would be greatly appreciated.
You only need to verify that these sets are groups,
that is
(1)
(2)
((3) associativity is automatically satisfied)
These are trivial exercises. Keep the definition of intersections in mind.
The same goes for
(Edit: What you wrote was not the right symbol for Union. The union symbol is . However the excercise is the same)