q11-relationapp - this digraph ±atherOf= John Mary John...

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CSE 260 QUIZ-11– Relations Applications- ANSWERS (20 minutes) NAME: 1. Compute the transitive closure of the Relation= { (1 , 2) , (1 , 3) , (2 , 3) , (3 , 4) , (3 , 2) } de- Fned over the set { 1 , 2 , 3 , 4 } using the algorithm given below. Procedure transitiveclosure ( M R : zero-one nxn matrix) A := M R B := A for i:=2 to n begin A := A ¯ M R B := B A end { B is the zero-one matrix for R * } $A1=B1=MR= 0 1 1 0 i=2, A2=A1 O MR= 0 0 1 1 B2=B1 V A2= 0 1 1 1 0 0 1 0 0 1 0 0 0 1 1 0 0 1 0 1 0 0 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 i=3, A3=A2 O MR= 0 1 1 0 B3=B2 V A3= 0 1 1 1 0 0 1 0 0 1 1 0 0 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 B3=B2, therefore, B4=B3. 2. Compute the transitive closure for the relation ±atherOf, given below, deFned over the set persons= { John, Mary, steve, Justin, Ned, Sam, Linda } : You draw the digraph for the relation Frst and then Fnd the transitive closure from
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Unformatted text preview: this digraph. ±atherOf= { John, Mary ) , ( John, steve ) , ( steve, Ned ) , ( Ned, Sam ) , ( Sam, Linda ) } What is the real world meaning of this transitive relation. SEE NEXT PAGE John Mary Steve Justin Ned Sam Linda TRANSITIVE CLOSURE: All pairs of nodes which are up to 6 (i.e., 7-1) hops away from each other because there are 7 nodes. { ( John, Mary ) , ( John, steve ) , ( steve, Ned ) , ( Ned, Sam ) , ( Sam, Linda ) , ( John, Ned ) , ( Steve, Sam ) , ( Ned, Linda ) , ( John, Sam ) , ( Steve, Linda ) , ( John, Linda ) } Real world meaning of the relation created by this transitive closure: AncestorOf...
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q11-relationapp - this digraph ±atherOf= John Mary John...

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