Practice Construction Of Hasse Diagrams (23.3.1) - Partial Ordering

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6 sample questions

Question 1.
What does it mean for a relation to be reflexive?
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Think about how every number relates to itself.
Question 2.
Can you provide an example of an antisymmetric relation?
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Refer back to our integer examples.
3Question 3.
What does antisymmetry imply in a partial order?
- If aRb and bRa
- then a = b
- If aRb
- then a < b
- All elements are comparable
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Focus on the nature of mutual relationships.
4Question 4.
True or False: A Hasse diagram must include self-loops for every element.
- True
- False
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Consider the properties of reflexivity involved in the diagram.
Question 5.
Given the set {2, 4, 5, 10, 20} and the relation 'divides', construct the Hasse diagram showing all relationships.
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Focus on which numbers divide which and build step by step.
Question 6.
Using the set {then, when, where} create a Hasse diagram reflecting the inclusion of subsets.
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Remember that every subset is part of the larger set.

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