Page No 5:
Question 5:
Check whether the relation R in R defined as R = {(a, b): a ≤ b3} is reflexive, symmetric, or transitive.
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.
