Practice Total Ordering And Hasse Diagram (24.5.2) - Cover of an Element in a Poset

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6 sample questions

Question 1.
Define a poset.
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Think of the properties that a relation needs.
Question 2.
What does it mean for y to cover x?
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Visualize this in a Hasse Diagram.
3Question 3.
What does a Hasse diagram represent?
- A type of graph
- A graph showing a poset
- A sorting algorithm
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Think about its purpose.
4Question 4.
True or False? Every poset must have both a least and a greatest element.
- True
- False
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Consider the definitions of these elements.
Question 5.
Create a Hasse diagram for the set of integers from 1 to 5 under the relation of 'divides'. Identify minimal and maximal elements.
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Take each number and see which others it divides.
Question 6.
Given a set of tasks: {A, B, C, D}, with dependencies: A must complete before B and C, C must complete before D; demonstrate a topological sort.
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Find all paths that respect the order of dependency.

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