A relation R on a set S is called a partial. ordering if it is reflexive, antisymmetric and transitive
1) reflexive:- binary relation R over a set X is reflexive if ∀x ∈ X : x R x
x R x ie x=2x which is not satisfy
so not reflexive
2) anti symmetric :-R is anti-symmetric precisely if for all x and y in X. if x R y and y R x then x =y
x R y: x=2y
and y R x: y=2x
it does not mean that x=y
so not antisymmetric
3) transtive:- if x R y and y R x then x R Z
x R y:x=2y
y R z: y=2z
then from above x=4z (but not x=2z for the condition x R z)
so not transitive
so not POSET