Practice Cover Of An Element In A Poset (24.1) - Cover of an Element in a Poset - part B

Practice: Cover of an Element in a Poset

Lesson 24.1Cover of an Element in a Poset - part B

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9 questions

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3 questions · about 2 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
Define what it means for one element to cover another in a poset.
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Think of the direct relationship without anything in between.
Question 2.
What is a maximal element?
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It’s at the top of the hierarchy in the poset.
3Question 3.
What defines a cover in a poset?
- x is less than y with intermediates
- x is related to y with no intermediates
- y is less than x with intermediates
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Think of direct connections in Hasse diagrams.
4Question 4.
In a poset, can an element be both a maximal and minimal element?
- True
- False
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Consider simple cases with one item in a poset.
Question 5.
Given the elements {1, 2, 3, 4, 5}, with the following relationships: 1 < 2, 1 < 3, 2 < 4, 3 < 4, and 3 < 5, define the covers of each element.
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Visualize with Hasse diagrams to track relations directly.
Question 6.
Construct a Hasse diagram for the elements A, B, C, D with the following relation: A < B, A < C, B < D, C < D. Identify maximal and minimal elements.
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Remember; stack based on relationships.

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