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 $A_1 B$ if $\left(A \cap B^c\right) \cup\left(B \cap A^c\right)=\emptyset$ and $A_2 B$ if $A \cup B^c=B \cup A^c, \forall A, B \in P(S)$. Then :