A relation R defined on the set A = {1,2,3,.....13,14} defined as R ={(x,y): 3x -y =0} is-

neither reflexive, nor symmetric, nor transitive.

A = {1,2,3,.....13,14} 

R ={(x,y): 3x -y =0} 

So, R ={(1,3), (2,6), (3,9), (4,12)}

R is not reflexive since (1,1), (2,2)....(14,14) ∉R

Also, R is not symmetric as (1,3) ∈R, but (3,1) ∉R . [3(3) - 1 ≠0]

Also, R is not transitive as (1,3), (3, 9) ∈R but (1,9) ∉R . [3(1)-9≠0]] 

Hence R is neither reflexive,  not symmetric, not rtransitive.