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

Question 5: Check whether the relation R in R defined as R = {(a, b): a ≤ b³} is reflexive, symmetric or transitive.

Answer: R = {(a, b): a ≤b³}

It is observed that

Therefore R is not reflexive.

Now,

(1, 2) ∈R (as 1 < 2³ = 8)

But,

(2, 1) ∉ R (as 2 > 1³ = 1)

∴R is not symmetric.

Now
 

∴R is not transitive.

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