If R be a relation from A = 1, 2, 3, 4 to B = 1, 3, 5 such that (a,...

$A = { 1, 2, 3, 4 }$~and~$B = { 1, 3, 5 }$

$∴ R = { ( 1, 3 ) , ( 1, 5 ) , ( 2, 3 ) , ( 2, 5 ) , ( 3, 5 ) , ( 4, 5 ) }$

and~$R^{- 1} = \left\{( 3, 1 ) , ( 5, 1 ) , ( 3, 2 ) , ( 5, 2 ) , ( 5, 3 ) , ( 5, 4 )\right\}$

Now,~

$3\overset{R- 1}{→}1\overset{R}{→}3 ⇒ \left(3, 3\right) \in ROR^{- 1}$

$5\overset{R- 1}{→}1\overset{R}{→}5 ⇒ \left(5, 5\right) \in ROR^{- 1}$

$5\overset{R- 1}{→}2\overset{R}{→}3 ⇒ \left(5, 3\right) \in ROR^{- 1}$

$3\overset{R- 1}{→}1\overset{R}{→}5 ⇒ \left(3, 5\right) \in ROR^{- 1}$

$∴ ROR^{- 1} = \left\{\left(3, 3\right), \left(3, 5\right), \left(5, 3\right), \left(5, 5\right)\right\}$