#### Question

Given an example of a relation. Which is Symmetric but neither reflexive nor transitive.

#### Solution

Let *A* = {5, 6, 7}.

Define a relation R on* A* as R = {(5, 6), (6, 5)}.

Relation R is not reflexive as (5, 5), (6, 6), (7, 7) ∉ R.

Now, as (5, 6) ∈ R and also (6, 5) ∈ R, R is symmetric.

=> (5, 6), (6, 5) ∈ R, but (5, 5) ∉ R

∴R is not transitive.

Hence, relation R is symmetric but not reflexive or transitive.

Is there an error in this question or solution?

Solution Given an Example of a Relation. Which Is Symmetric but Neither Reflexive Nor Transitive. Concept: Types of Relations.