Is it possible to have a relation on the set {a, b, c} that is both symmetric and transitive but not reflexive

Yes, it is possible to have  a relation on the set {a, b, c} that is both symmetric and transitive but not reflexive

Step-by-step explanation:

Let

Set A={a,b,c}

Now, define a relation R on set A is given by

R={(a,a),(a,b),(b,a),(b,b)}

For reflexive

A relation is called reflexive if (a,a) for every element a

Therefore, the relation R is  not reflexive.

For symmetric

If then

We have

and

Hence, R is symmetric.

For transitive

If (a,b) and (b,c) then (a,c)

Here,

and

and

Therefore, R is transitive.

Yes, it is possible to have  a relation on the set {a, b, c} that is both symmetric and transitive but not reflexive.

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