a) To provide example of a relation,which is reflexive and symmetric but not transitive. Reflexive property, a = a Symmetric property, if a=b then b=a Transitive property, if a=b and b=c, then a must be equal to c . Consider the below given relation for reflexive and symmetric but not for transitive, R = { ( a , a ) , ( a , b ) , ( b , a ) , ( b , b ) , ( c , c ) , ( b , c ) , ( c , b ) } The above set is reflexive as for all a there is a relation ( a , a ) , for all b there is a relation ( b , b ) and for all c there is a relation ( c , c ) The above given set is also follows symmetric property, For a relation ( a , b ) there is a relation ( b , a ) , for all relation ( b , c ) there is a relation ( c , b ) . But this relation is not transitive as there is ( a , b ) and ( b , c ) but no set of ( a , c ) . b) To provide example of a relation, which is reflexive and transitive but not symmetric. Conditions- Reflexive property, a = a Symmetric property, if a=b then b=a Transitive property, if a=b and b=c, then a must be equal to c . Consider the below given relation for reflexive and transitive but not for symmetric, R = { ( a , a ) , ( a , b ) , ( a , c ) , ( b , b ) , ( c , c ) , ( b , c ) } The above set is reflexive as for all a there is a relation ( a , a ) , for all b there is a relation ( b , b ) and for all c there is a relation ( c , c ) This relation is transitive there is relation ( a , c ) for ( a , b ) and ( b , c ) realtions. The above given set does not follows symmetric property, As for a relation ( a , b ) there is norelation ( b , a ) , for all relation ( b , c ) there is no relation ( c , b ) . c) To provide example of a relation, which is symmetricand transitive but notreflexive. Reflexive property, a = a Symmetric property, if a=b then b=a Transitive property, if a=b and b=c, then a must be equal to c . Consider the below given relation for symmetricand transitive but not for reflexive, R = { ( a , b ) , ( b , a ) , ( b , c ) , ( c , b ) } The above given set follows symmetric property, As for a relation ( a , b ) there is relation ( b , a ) , and for relation ( b , c ) there is relation ( c , b ) This relation is transitive there is relation ( a , c ) for ( a , b ) and ( b , c ) relations. The above set is not reflexive as for a there is no relation ( a , a ) , for all b there is no relation ( b , b ) and for all c there is no relation ( c , c ) .

Introduction to Algorithms

3rd Edition

ISBN: 9780262033848

Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein

Publisher: MIT Press

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