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Unformatted text preview: 1. Program modules can import other modules. [You have seen this al ready in the Haskell course.] They can also depend indirectly on mod ules via some chain of importation, so that for instance M depends on M if M imports M and M imports M . The relation depends is the transitive closure of the relation imports. 2. Two people are related if one is the parent of the other, if they are mar ried, or if there is a chain of such relationships joining them directly. We can model this by a universal set People , with three relations Mar ried , Parent and Relative . The relation Relative is defined using the transitive closure: Relative = (( Parent Parent 1 ) Married ) + D EFINITION 3.16 (T RANSITIVE C LOSURE ) Let R be a binary relation on A . The transitive closure of R , written t ( R ) or R + , is n 1 R n : that is, R R 2 R 3 R 4 . . . The transitive closure of a binary relation always exists. To cast more light on R + , we now examine an alternative way of building the transitive clo...
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This note was uploaded on 01/02/2010 for the course MATH Math2009 taught by Professor Koskesh during the Spring '09 term at SUNY Empire State.
 Spring '09
 Koskesh
 Math

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