$A=\{2,3,4,6,8,12\},\ x,y \in A, x\le y \leftrightarrow x^2 \mid y$
Is this a partial order and draw the Hasse diagram.
I know to be a partial order it needs to be reflexive, anti symmetric and transitive. I have the solutions to this problem but I do not seem to understand why it is not reflexive and how to draw the Hasse diagram for $A$.
Solution: not a partial order( since not reflexive, not anti symmetric, and transitive).
It is not reflexive because for example, putting $x:=y:=2\in A$, they won't be in relation to each other as $2\cdot 2 \nmid 2$. Same for anti-symmetric, use $2$ and $4$.