What is the difference between an identity relation and a reflexive relation?
Asked by joykphukan | 1st May, 2015, 12:37: PM
Expert Answer:
An identity relation on a set 'A' is the set of ordered pairs (a,a), where 'a' belongs to set 'A'.
For example, suppose A={1,2,3}, then the set of ordered pairs {(1,1), (2,2), (3,3)} is the identity relation on set 'A'.
Any relation 'R' on a set 'A' is said to be reflexive if (a,a) belongs to 'R', for every 'a' belongs to set 'A'.
For example, suppose A={1, 2, 3}, then a relation 'R' defined by R={(1,1), (2,2), (3,3), (1,3), (3,2)} is a reflexive relation.
There can be MANY reflexive relations defined on a set. But, an identity relation on any set is UNIQUE.
Answered by satyajit samal | 2nd May, 2015, 02:07: PM
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