okay,transitive closure is the relations, which after adding to an existing relation,the entire relation will be Transitive relation..
let R={(1,2)(1,1)} is a given relation...
now Transitive closure of this relation is the relations that needs to be added to make a transitive relation of element 1,2
now if we add (2,1)(2,2) to the existing R, the entire R will be transitive
so {(2,1)(2,2) } is the transitive closure
Hope this helps