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R = {(1,1),(2,1),(3,2),(4,3)}
R2  = R * R = { (1,1), (2,1) , (3,1), (4,2) }
R3 = R* R = { (1,1), (2,1), (3,1), (4,1) }

R U RU R= {(1,1), (2,1) , (3,1), (3,2), (4,1), (4,2),(4,3) }

To find the R*R search for the  terms like  (X,Y) (Y,Z)  which convert to  (X,Z).

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