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Which are the minimal and maximal elements?

The poset is: $(\{\emptyset,\{{\emptyset,1 \},\{1\}},\{1,2\}\},\subseteq) $

I assume, that it will look like a vertical chain, at the first stage from below with $\emptyset$, the second, $ \{\emptyset,1 \} $, the third $ \{1\}$, and the last one which is at the top of the chain will be $\{1,2\}$.

How could I draw Hasse-diagram with latex, is my solution correct in this way?

Herrpeter
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1 Answers1

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we have $$(\{\emptyset, \{\emptyset, 1\}, \{1\}, \{1, 2\}\}, \subset)$$

At the very bottom we should have $\emptyset$ because $$\emptyset \subset \{\emptyset, 1\}$$ $$\emptyset \subset \{1\}$$ $$\emptyset \subset \{1, 2\}$$

Then we have $\{1\}$ which should be straight up from there (nothing else at that level) $$\{1\} \subset \{\emptyset, 1\}$$ $$\{1\} \subset \{1, 2\}$$

after that, we have two maximal elements $\{1, 2\}$ and $\{\emptyset, 1\}$

The lines should look like this:

\ /

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Flasgod
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  • I appreciate your fast answer, and can I say that $\emptyset$ is the minimal element? – Herrpeter Apr 26 '17 at 17:42
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    yes, it is the minimal and the minimum (there's no maximum because there's two maximals and maximums must be unique). – Flasgod Apr 26 '17 at 17:46