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Question
Defines a relation on N :
x + y = 10, x, y∈ N
Determine the above relation is reflexive, symmetric and transitive.
Solution
We have,
R = {(x, y) : x + y = 10, x, y ∈ N}
R= {(1,9),(2,8),(3,7),(4,6),(5,5),(6,4),(7,3),(8,2),(9,1)}
As, (1,1) ∉ R
So, R is not a reflexive relation
Let (x,y) ∈ R
⇒ x+y = 10
⇒ y+x = 10
⇒ (y,x) ∈R
So, R is a symmeteric relation
As, (1,9) ∈ R and (9,1) ∈ R but (1,1) ∉ R
So, R is not a transitive relation
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