Find an example of a single nonempty relation R which is bot

Find an example of a single non-empty relation R which is both symmetric and anti-symmetric. If this is not possible explain why.

Solution

Let A={1,2,3} and R= {(1,1),(2,2)} be a relation on A.

Symmetric Property: since 1 is related 1 and 2 is related 2, R satisfies the symmetric property. (by Symmetric Property: If a R b then b R a)

Anti- Symmetric Property: : since 1 is related 1 and 2 is related 2, R satisfies the symmetric property. (by Symmetric Property: If a R b and b R a then a R a)