Practice Steps Of The Algorithm (24.4.2) - Cover of an Element in a Poset

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6 sample questions

Question 1.
Define a cover in the context of posets.
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Think about the direct relationship in a staircase.
Question 2.
What is a maximal element?
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Is there anything above a maximal element in the hierarchy?
3Question 3.
What is the condition for an element y to cover element x?
- y must be less than x
- x ≤ y and no element z such that x ≤ z ≤ y
- y must be equal to x
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Remember, it's about the lack of intermediates.
4Question 4.
True or False: An element can be both maximal and minimal.
- True
- False
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Consider if an element stands alone.
Question 5.
Construct a Hasse diagram for the following set of relationships: {1, 2, 3, 4} with the relationships 1 < 2, 1 < 3, 2 < 4.
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Consider each relationship to lay out the elements.
Question 6.
Given the tasks A, B, C, and D where A must occur before B and C, and B must occur before D, list a valid topological order.
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Start with the task that has no dependencies.

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