A. $R \cap S = ( R \cup S) - [(R-S) \cup (S-R)]$
{ 2 } = { 1 , 2 , 3 } - [ {1} ∪ {3} ]
{ 2 } = { 2 }
B. $R \cup S = ( R \cap S) - [(R-S) \cup (S-R)]$
{ 1 , 2 , 3} ≠ { 2 } - [ 1,3 ]
C. $R \cap S = ( R \cup S) - [(R-S) \cap (S-R)]$
{ 2 } ≠ { 1 , 2 , 3 } - [ 1 ∩ 3 ]
D. $R \cap S = ( R \cup S) \cup (R-S)$
{ 2 } = { 1 , 2 , 3 } ∪{1}
{ 2 } ≠ { 1 , 2 , 3 }
Hence.Option(A) $R \cap S = ( R \cup S) - [(R-S) \cup (S-R)]$ is the correct choice.