Question

Check whether the relation R in R defined as R = {(a, b): a ≤ b³} is reflexive, symmetric or transitive.

Answer 1

R = {(a, b): a ≤ b³}
It is observed that (1/2,1/2)∉R, since, 1/2>(1/2)³
∴ R is not reflexive.

∴ R is not transitive.
Hence, R is neither reflexive, nor symmetric, nor transitive.