Each of the following defines a relation on N:

x + 4y = 10 x, y ∈N.


Determine which of the above relations are reflexive, symmetric and transitive.

Let R = {(x,y): x + 4y =10, ∀ x,y ∈ N } be a relation defined on N.


R = {(2,2),(6,1)}


Now,


R is not reflexive ∵ (1,1) ∉ R.


R is not symmetric ∵ (6,1) ∈ R but (1,5) ∉ R


R is not transitive


∵ (x,y) ∈ R ⇒ x+4y=10 and (y,z) ∈ R ⇒ y+4z=10


⇒ x-16z = -30


⇒ (x,z) ∉ R


Thus, R is neither symmetric nor reflexive nor transitive.


23