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2015-04-18T16:00:37+05:30

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

Get R^{-1} by swapping coordinates :
R^{-1}=\{(3,1),(5,1),(3,2),(5,2),(5,3),(5,4)\}

the composition R\,\circ\,R^{-1} can be obtained by seeing the possible points of R for each value of R^{-1} :
 R^{-1}(3)=1,2\implies\,R\,\circ\,R^{-1}(3)=R(1),R(2)=3,5

that means, the composition R\,\circ\,R^{-1} maps 3 to 3 or 5. therefore you get points (3,3) and (3,5)
2 5 2
5 ------>R^(-1)------->1 or 2-------R-------> 3 or 5
therefore RoR^(-1)(5) = 3 or 5
and you get points (5, 3) and (5, 5)
got it thanks a lot
np:)