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

∴ R is not reflexive.

Now,

(1, 2) ∈ R (as 1 < 2³ = 8)

But,

(2, 1) ∉ R (as 2 > 1³ = 1)

∴ R is not symmetric.

We have

But

∴ R is not transitive.

Hence, R is neither reflexive, nor symmetric, nor transitive.