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 \( (A\cap B^{c})\cup(B\cap A^{c})=\varnothing \) and \( A R_{2} B \) if \( A\cup B^{c}=B\cup A^{c} \), \( \forall A,B\in P(S) \). Then:
