Let a relation R be defined by relation The `R = {(4, 5), (1,4), (4, 6), (7, 6), (3,7)}` `R^(-1)oR` is given by

Explanation

`(i)R= {(4,5),(1,4),(4,6),(7,6),(3,7)}`
`rArrR^(-1)={(5,4),(4,1),(6,4),(6,7),(7,3)}`
Now, `(5,4)in R^(-1)and (4,1)in R^(-1)`
`rArr (5,1)in R^(-1)oR^(-1)`
`(6,4)in R^(-1)and (4,1)in R^(-1)rArr(6,1)in R^(-1)oR^(-1)`
`(6,7)inR^(-1) and (7,3)in R^(-1)rArr(6,3)in R^(-1)oR^(-1)` Ans.
`:.R^(-1)oR^(-1)={(5,1),(6,1),(6,3)}`
(ii) `(R^(-1)oR)^(-1) = R^(-1)o(R^(-1))^(-1)=R^(-1)oR`
R = {(4,5),(1,4),(4,6),(7,6),(3,7)}
`R^(-1)`= {(5,4),(4,1),(6,4),(6,7),(7,3)}
Reprsentation on a diagram
`:. (R^(-1)oR)^(-1) = R^(-1)oR`
= {(1,1),(3,3),(4,4),(4,7),(7,4),(7,7)}. Ans.