Question

Determine whether each of the follow relations are reflexive, symmetric and transitive: 

(i) Relation R in the set A = {1,2,3,13,14} defined as R = {(x, y): 3x – y = 0}

Answer 1

A = {1, 2, 3,………. 14} 

R={(x, y) : 3x – y = 0} 

= {(x, y) : y = 3x) 

R : {(1,3), (2,6), (3,9), (4,12)} 

R is not reflexive as (1,1) ∉ R 

R is not symmetric as (1,3) ∈ R but (3,1) ∉ R 

R is not transitive as (1,3) ∈ R, (3,9) ∈ R but (1, 9) ∉ R. 

To disprove, any counter example is sufficient.