Question

Let a relation R be defined by R = {(4,6); (1,4); (4,6); (7,6); (3,7)} then $R^{-1}$ oR is

• A. {(1, 1), (4, 4), (4, 7), (7, 4), (7, 7), (3, 3)}
• B. {(1, 1), (4, 4), (7, 7), (3, 3)}
• C. {(1, 5), (1, 6), (3, 6)}
• D. None of these

Answer 1

The correct option is A

{(1, 1), (4, 4), (4, 7), (7, 4), (7, 7), (3, 3)}

We first find $R^{-1}$ , we

have $R^{-1}$ = { (5,4);(4,1);(6,4);(6,7);(7,3)}. We now obtain the elements

of $R^{-1}$ oR we first pick the element of R and then of R^{-1}.Since (4,5) $\in$ R and (5,4) $\in$ $R^{-1}$ , we have (4,4) $\in$ $R^{-1}$oR

Similarly , (1,4) $\in$ R , (4,1) $\in$ $R^{-1}\Rightarrow (1,1)\in R^{-1}oR$

(4,6) $\in R(6,4)\in R^{-1}\Rightarrow (4,4)\in R^{-1}oR,$

(4,6) $\in R(6,7)\in R^{-1}\Rightarrow (4,7)\in R^{-1}oR,$

(7,6) $\in R(6,4)\in R^{-1}\Rightarrow (7,4)\in R^{-1}oR,$

(7,6) $\in R(6,7)\in R^{-1}\Rightarrow (7,7)\in R^{-1}oR,$

(3,7) $\in R(7,3)\in R^{-1}\Rightarrow (3,3)\in R^{-1}oR,$

Hence , $R^{-1}oR$ = { (1,1); (4,4); (4,7); (7,4), (7,7); (3,3)},