Let R be relation defined on the set of natural number N as follows:

Given function: R = {(x, y): x ∈ N, y ∈ N, 2x + y = 41}.

So, the domain = {1, 2, 3, ….., 20} [Since, y ∈ N ]

Finding the range, we have

R = {(1, 39), (2, 37), (3, 35), …., (19, 3), (20, 1)}

Thus, Range of the function = {1, 3, 5, ….., 39}

R is not reflexive as (2, 2) ∉ R as 2 x 2 + 2 ≠ 41

Also, R is not symmetric as (1, 39) ∈ R but (39, 1) ∉ R

Further R is not transitive as (11, 19) ∉ R, (19, 3) ∉ R; but (11, 3) ∉ R.

Thus, R is neither reflexive nor symmetric and nor transitive.