On rt on a sasfying the following three properes 1 rt

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Unformatted text preview: •  Defini.on: Let R be a binary rela.on on a set A. The transi.ve closure of R is the binary rela.on Rt on A sa.sfying the following three proper.es: 1. Rt is transi.ve 2. R is a subset of Rt 3. If S is any other transi.ve rela.on that contains R, then S contains Rt . • In other words, the transi.ve closure of R is the smallest transi.ve rela.on containing R. 3 Sangmi Lee Pallickara CS480 Principles of Data Management 2 Sangmi Lee Pallickara Spring 2013 Example of the Transitive Closure 4 Sangmi Lee Pallickara CS480 Principles of Data Management Spring 2013 The relationship “is-duplicate-of” •  Given the rela.on R on {1,2,3,4}, •  Is transi.ve. 1 4 –  Candidate 3 is a duplicate of candidate 5 –  Candidate 3 is a duplicate of candidate 6 –  Candidate 5 and 6 are duplicate 2 3 •  its transi.ve closure is: 1 2 4 3 Sangmi...
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