Let \(P(S)\) denote the power set of \(S=\{1,2,3, \ldots, 10\}\). Define the relations \(R_1\) and \(R_2\) on \(P(S)\) a…

Let \(P(S)\) denote the power set of \(S=\{1,2,3, \ldots, 10\}\). Define the relations \(R_1\) and \(R_2\) on \(P(S)\) as \(A R_1 B\) if \(\left(A \cap B^c\right) \cup\left(B \cap A^c\right)=\phi\) and \(A R_2 B\) if \(A \cup B^c=\) \(B \cup A^c, \forall A, B \in P(S)\). Then:

[JEE Main 2023, 1 Feb (Shift 2)]