Q. 115.0( 1 Vote )

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

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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Fill in the blanks in each of the

Let the relation R be defined on the set

A = {1, 2, 3, 4, 5} by R = {(a, b) : |a^{2} – b^{2}| < 8}. Then R is given by _______.

State True or False for the statements

Every relation which is symmetric and transitive is also reflexive.

Mathematics - ExemplarState True or False for the statements

Let R = {(3, 1), (1, 3), (3, 3)} be a relation defined on the set A = {1, 2, 3}. Then R is symmetric, transitive but not reflexive.

Mathematics - ExemplarState True or False for the statements

An integer m is said to be related to another integer n if m is a integral multiple of n. This relation in Z is reflexive, symmetric and transitive.

Mathematics - Exemplar