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

Answer
Method -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 2³ > 1)
∴ R is not symmetric. We have

 But
 ∴ R is not transitive. Hence, R is neither reflexive, nor symmetric, nor transitive.
Method - 2

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

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