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27 - Manchester Knock London Dubin Paris Edinburgh Rome...

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London Edinburgh Manchester Dubin Knock Paris Rome Madrid Define the relation R + by a R + b if and only if there is a trip from a to b . Then clearly a R + b if and only if there is some path from a to b in the directed graph. For instance, there is a path from Manchester to Rome, but no path from Rome to Manchester. We would like to calculate R + from R . Such a relation is called the transitive closure of R , since it is clearly transitive, and is in fact a special relation in the sense that it is the smallest transitive relation containing R . We can express the relation R + in terms of R using relational composi- tion: a R + b if and only if there is a path of length n
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