NDA Math Sets Relations and Functions

Give set S={1,2,3,....}
For xRy,logax>logay
⇒x>y
As xRx,logax>logax is not valid.
Hence, relation is not reflexive.
For xRy,logax>logay ⇒x>y
yRx,logay>logax ⇒y>x
This is also not valid. Hence, relation is not symmetric also.
For xRy,logax>logay ⇒x>y
For yRz,logay>logaz ⇒y>z
So, xRz,logax>logaz ⇒x>z
This is a valid relation.
Hence, relation is only transitive.