Question

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

Answer 1

(a, a) ∈ R 

∴ not reflexive 

a= 1, b = 2 

(a, b) ∈ R ⇒<8 

(b, a) ∈ R 2 ≤ 1, which is not true 

(a, b) ∈ R ⇒ (b, a) ∈ R, hence not symmetric 

a = 60, b = 4, c = 3 

60 ≤ 4³ , 4 ≤ 3³ 60 ≤ 3³ 

(a, b) ∈ R, (b, c) ∈ R  (a, c) ∈ R. 

hence R is not transitive.