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Exercise 28 - Chapter 1

Let \(X\) be the set of partitions of {•,◦,∗}; it has five elements and an order by coarseness, as shown in the Hasse diagram Eq. (1.2). Write down every pair \( (x,y) \) of elements in \(X\) such that \(x≤y\). There should be 12.

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  • 1.
    edited April 2018

    Figure

    \( (x2, x1) , (x3, x1), (x4, x1), (x5, x1), (x5, x2), (x5, x3), (x5, x4), (x1, x1), (x2, x2), (x3, x3), (x4, x4), (x5, x5) \)

    Are the arrows backwards? Is \( \text{ more coarse } \le \text{ more fine } \) ?

    Comment Source:![Figure](https://docs.google.com/drawings/d/e/2PACX-1vSHvXcWpaxv-VMyJY037GdPlW4NN85kZ6WWgzLbZ1VWlQJ0jZ0BjwZNmiCJ3Vv3J5acg31H1BpGYICR/pub?w=502&h=383) \\( (x2, x1) , (x3, x1), (x4, x1), (x5, x1), (x5, x2), (x5, x3), (x5, x4), (x1, x1), (x2, x2), (x3, x3), (x4, x4), (x5, x5) \\) Are the arrows backwards? Is \\( \text{ more coarse } \le \text{ more fine } \\) ?
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