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Question
Defines a relation on N :
x > y, x, y ∈ N
Determine the above relation is reflexive, symmetric and transitive.
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Solution
We have,
R = {(x, y) : x > y, x, y ∈ N}
As, x = x ∀x ∈ N
⇒ (x,x) ∉ R
So, R is not a reflexive relation
Let (x,y) ∈ R
⇒ x > y
but y < x
⇒ (y,x) ∉ R
So, R is not a symmeteric relation
Let (x,y)∈R and (y,z) ∈ R
⇒ x > y and y > z
⇒ x > z
⇒ (x,z) ∈ R
So, R is a transitive relation
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