Consider the set G = {0,{1},{2},{1,2}}. Does the set operation intersection define a binary operation on G? Does the set operation union define a binary operation on G? Is < G,(union) > a group? Explain. Is < G, (intersection) > a group? Explain.
So I know that a binary operation takes all possible ordered pairs of elements of G and outputs an element of the set G. However, I do not understand how to apply this in this context... I also know that in order to be a group it is necessary that: the group is closed under a binary operation associative: (a*b)c= a(b*c) identity: contains the identity element e inverse: for every a in G, a^-1 is also in G