G is the set of all subset of A. (For example - Say $A=\{1,2,3\}$ than $G=(\{1\},\{2\},\{3\},\{1,2\}...)$. ($A$ is at east two different elements).
the binary operation $*$ is intersection. I need to prove this is a group .
Identity element - will be the empty set.
Associative-Yes
Inverse element - Yes . I need that For each $g\in G$, there must be an element $g^{-1}\in G$ so that $g^{-1}*g=g*g^{-1}=e$. I think the empty set do that as well.
until here I hope I was right.
Now I want to show if this is finite or abelian.
Abelian - Yes- easy to show.
But now Im not sure if this is finite and how to show that...