Section 1.5: Misc Exercises

Given a non-empty set \(X\), consider \(P(X)\) which is the set of all subsets of \(X\).

Define the relation \(R\) in \(P(X)\) as follows:
For subsets \(A, B\) in \(P(X)\), \(A R B\) if and only if \(A \subseteq B\).
Is \(R\) an equivalence relation on \(P(X)\)? Justify your answer.