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$\begingroup$

$A=\{2,3,4,6,8,12\},\ x,y \in A, x\le y \leftrightarrow x^2 \mid y$

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).

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    I edited your post. Check whether the edited version represents what you intended, since the original could have been interpreted as in my edit or as $xx\;|\;y$.2012-10-15
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    But.. plainly $|$ is a partial order, I think indeed $x^2|y$ was meant..2012-10-15
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    @Berci. You're right of course, $|$ is indeed a partial order, but look at the source of the original.2012-10-15

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