Question

Check whether the relation R defined in the set {1, 2, 3, 4, 5, 6} as R = {(a, b) : b = a + 1} is reflexive, symmetric or transitive.

Answer 1

R = {(1, 2), (2, 3), (3, 4), (4, 5), (5, 6)} 

R is not reflexive as (1, 1) ∉ R 

R is not symmetric as (1, 2) ∈ R  (2,1) ∈ R 

R is not transitive as (2, 3) ∈ R, (3, 4)e 

R ⇒(2,4) ∈ R