Q. 115.0( 1 Vote )

Is it true that e

Answer :

It is not true that every relation which is symmetric and transitive is also reflexive.

Take for example:


Take a set A = {1, 2, 3, 4}


And define a relation R on A.


Symmetric relation:


R = {(1, 2), (2, 1)}, is symmetric on set A.


Transitive relation:


R = {(1, 2), (2, 1), (1, 1)}, is the simplest transitive relation on set A.


R = {(1, 2), (2, 1), (1, 1)} is symmetric as well as transitive relation.


But R is not reflexive here.


If only (2, 2) R, had it been reflexive.


Thus, it is not true that every relation which is symmetric and transitive is also reflexive.


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