Show that the relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} is symmetric but neither reflexive nor transitive.

Let us take A = {1, 2, 3}

A relation R is defined on set A as R = {(1,2), (2,1)}

It is seen that (1,1), (2,2), (3,3) ∉ R.

Therefore, R is not reflexive.

Now, we can see that (1,2) ϵ R and (2,1) ϵ R

Therefore, R is symmetric.

And now, (1,2), (2,1) ϵ R

But, (1,1) ∉ R

Therefore, R is not transitive.

Therefore, R is symmetric but neither reflexive, nor transitive.