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Question
Defines a relation on N :
xy is square of an integer, x, y ∈ N
Determine the above relation is reflexive, symmetric and transitive.
Solution
We have,
R = {(x, y) : xy is square of an integer, x, y ∈ N}
As, x×x=x2, which is a square of an integer x
⇒ (x,x) ∈ R
So, R is a reflexive relation
Let (x,y) ∈ R
⇒ xy is square of an integer
⇒ yx is also a square of an integer
⇒ (y,x) ∈ R
So, R is a symmeteric relation
Let (x,y) ∈ R and (y,z) ∈ R
⇒xy is square of an integer and yz is also a square of an interger
⇒ xz must be a square of an integer
⇒ (x,z) ∈ R
So, R is a transitive relation
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