q10-relations

# q10-relations - CSE 260 QUIZ-10 Relations ANSWERS(30...

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CSE 260 QUIZ-10– Relations: ANSWERS (30 minutes/total 5 questions) NAME: 1. Following relation is defined on the set { 1 , 2 , 3 , 4 } . { (1 , 1) , (1 , 2) , (2 , 1) , (2 , 2) , (3 , 3) , (4 , 4) } Indicate, whether it is reflexive, whether it is symmetric, whether it is antisymmetric, and whether it is transitive. reflexive, symmetric, transitive 2. Following relation is represented by a matrix below. Circle the appropriate properties below for the relation. reflexive/NO symmetric/YES antisymmetric/NO transitive/NO | 1 2 3 4 ----------------------- 1 | 1 1 1 0 | 2 | 1 0 1 0 | 3 | 1 1 0 0 | 4 | 0 0 0 0 3. Following relation is represented by a directed graph (digraph). A B C D Circle the appropriate properties below for the relation. reflexive/NO irreflexive/NO symmetric/NO antisymmetric/YES asymmetric/NO transitive/NO irreflexive: No loop in any node. asymmetric: ( a, b ) R ( b, a ) ¬ R even if a=b Thus, asymmetric does not allow self-loop while antisymmetric does. Thus R is asymmetric if and only if R is antisymmetric and also irreflexive.

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4. Let R be the relation R = { ( a, a ) , ( b, a ) , ( c, b ) , ( d, c ) } . Find the powers R 2 , R 3 R 2 = { ( a, a ) , ( b, a ) , ( c, a ) , ( d, b ) } R 3 = { ( a, a
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