Q. 115.0( 1 Vote )

# Is it true that every relation which is symmetric and transitive is also reflexive? Give reasons.

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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