Q. 22 C5.0( 2 Votes )

Each of the follo

Answer :

Let R = {(x,y): x y is square of an integer, x,y N } be a relation defined on N.


R is reflexive x2 is square of an integer x N (x,x) R


Let (x,y) R x, y N


x y is square of an integer


y x is square of an integer


(y,x) R


R is symmetric


Let (x,y) R and (y,z) R x, y,z N


x y is square of an integer and yz is square of an integer


let xy = p2 and yz = q2 for some p,q Z



, which is square of an integer


(x,z) R


R is transitive.


Thus, R is reflexive, symmetric and transitive.


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