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 $A\,R_{1}\,B \iff (A\cap B^{c})\cup(B\cap A^{c})=\varnothing$ and $A\,R_{2}\,B \iff A\cup B^{c}=B\cup A^{c}$, for all $A,B\in P(S)$. Then: