Practice Properties Of Covers (24.1.2) - Cover of an Element in a Poset

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6 sample questions

Question 1.
What is a poset?
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Think about the properties that define relationships.
Question 2.
What does it mean when we say 'y covers x'?
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Visualize in terms of layers.
3Question 3.
What defines a cover in a poset?
- A relationship with a middle element
- Immediate upward relation with no intermediaries
- Directly connected elements only
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Think about Hasse diagrams.
4Question 4.
True or False: A poset can have multiple maximal elements.
- True
- False
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Recall the definition of maximal.
Question 5.
Construct a simple Hasse diagram for a poset containing the elements {1, 2, 3, 4} with the following relationships: 1 < 2, 1 < 3, 2 < 4, 3 < 4. Identify maximal and minimal elements.
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Draw it layer by layer and look for the top and bottom.
Question 6.
Given the elements {a, b, c, d} where a < b, a < c, b < d, but c is not related to d, demonstrate whether d can be a greatest element.
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Check the relationships to determine coverage.

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