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

Question

Check whether the relation R in R defined by R = {(a, b) : a ≤ b 3 } is reflexive, symmetric or transitive.

Philoid · Accepted Answer

It is given that R = {(a, b) : a ≤ b³}

Now, It can observed that as

Therefore, R is not reflexive.

Now, (1,3) ϵ R(as 1 < 3³ = 27)

But, (3,1) ∉ R(as 3³ > 1)

Therefore, R is not symmetric.

Now, if we have

Therefore, R is not transitive.

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

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