Text book Problem

In his research Prof. Ross considered the set P of all subsets of (for example, {5, 6, 7, 8} is such a subset). Then he considered a relation R from P to P (the shorthand for that statement is ”a relation R on P”) defined as follows: (A, B) ∈ R if A ⊆ B When writing the final version of their research paper, his assistant wrote (7, {5, 6, 7, 8, 9}) ∈ R Was the assistant correct or he made an error? If you think the assistant erred, explain why?

The set P is like {{1},{2},{3},…,{1,2},{1,3},…,{1,2,3},{1,2,3,4} ,…}. When we do a cartesian product with itself we get elements like {({1},{1,2,3}),({1},{2,3,4}),…}. Thus each element of an ordered pair is a set itself. So the assistant made a mistake it should have been ({7},{5,6,7,8,9}). Because