Additional problems: Let P(X) be the power set of a non-empty set X. 1. Consider (P(X),U), where U is the set union. Is it a group? How about (P(X),n), where n is the set intersection? Justify your answers. 2. Consider the group (P(X), A), where A is the symmetric difference of sets. Can you list all possible orders for the elements in this group? Justify your answer.