i have been reading diagram Hasse.My question is how i give position to numbers on diagram.Let me explain Example 1 :Lets say i have a set A={1,2,3,4,5,6,7,8} i will draw with the smallest part 1 and this will have 2 3 5 and 7.From up the 2 it will be have 4 and 8.Up to 3 it will have the 6.In 5 and 7 nothing.
Example 2:Lets say i have A={12,18,22,23,25,29,32,40} . I did this because on my exercise are simple.How can it be something like this?How i position the numbers?What i will do is starting point 12.Can it be something like this ? Could you explain me how i position the numbers because i am getting confused.Thanks
Consider two small examples: $A=\{1,2,3\}$ with partial order $R=\{(2,1),(2,3)\}$
Our Hasse Diagram will look like this:
$\begin{array}{ccc}1&&3\\ \backslash & & /\\&2\end{array}$
To craft the diagram, we not only need to know what the set is, but we also need to know what the order is. In this example $(2,1)\in R$ so $2$ should appear "below" $1$. Similarly $(2,3)\in R$ so $2$ should appear below $3$. $1$ and $3$ are not related however, so they should not have any lines comparing them. Note also, despite $1$ being the "smaller number" according to our usual description, that is irrelevant here.
Let $B=\{00,01,10,11\}$ with order $S=\{(00,01),(00,10),(00,11),(01,11),(10,11)\}$
Here we have our Hasse diagram like this:
$\begin{array}{ccc}&11\\/&&\backslash\\01&&10\\\backslash&&/\\&00\end{array}$
Note that in this example that although $00$ is below $11$, we don't bother drawing a line directly between them, this is taken care of by the fact that there are longer paths leading only upwards that you can take instead. Further, notice that both $01$ and $10$ are below $11$.
See more examples and more details in your textbook or on the wiki page.
As for your specific example you ask about, there is not enough information to begin constructing the diagram as it requires knowledge of what the order to be used is.