(x,y)∊S id x divides y. For x∊Z,x divides x. Hence,(x,x)∊s,∀x∊Z Hence,S is reflexive....(1)
If (x,y)∊S⇒x divides y⇒y=Kx Where K is an integer. ⇒x=
1
K
y,where
1
K
may not be an integer. Hence,y does not divide x. Hence,(y,x)∉S Hence,S is not symmetric...(2)
If (x,y)∊S and (y,z)∊S,then y=K1x and z=K2y(K1K2∊Z) ⇒z=K2K1x Hence,x divides z. Hence,(x,z)∊S Hence ,the given relation is transitive....(3) From (1)(2)(3) the given relation is only reflexive and transitive