The relation ''less than'' in the set of natural numbers is:

For any $x∈R$

$x<x$ (not possible), not reflexive

$(x,y)∈R⇒(y,x)∈R$

$x<y⇒y<x$ → not symmetric

$(x,y)∈R⇒(y,z)∈R$

$x<y,\,y<z$ → transitive onle

$⇒(x,z)∈R$