The relation R defined in the set N of natural numbers defined as R = {(x, y): y = x+ 5 and x <4} is-

Transitive only

R = {(x, y): y = x+ 5 and x <4} = {(1, 6), (2, 7), (3, 8) }

It is seen that (1, 1) ∉ R.

So, R is not reflexive.

(1, 6) ∈ R

But (6, 1) ∉ R.

So, R is not symmetric.

Now, since there is no pair in r such that (x, y) and (y, z) ∈ R so, we need not look for the ordered pair (x, z) in R.

So R is transitive.

Hence R is neither reflexive, nor symmetric but it is transitive only.