Sets and Relations

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 $\mathrm{AR}_{1} \mathrm{~B}$ if $\left(\mathrm{A} \cap \mathrm{B}^{\mathrm{c}}\right) \cup\left(\mathrm{B} \cap \mathrm{A}^{\mathrm{c}}\right)=\emptyset$ and $\mathrm{AR}_{2} \mathrm{~B}$ if $\mathrm{A} \cup \mathrm{B}^{\mathrm{c}}=\mathrm{B} \cup \mathrm{A}^{\mathrm{c}}, \forall \mathrm{A}, \mathrm{B} \in \mathrm{P}(\mathrm{S})$. Then :