Practice Maximal And Minimal Elements In A Poset (24.2) - Cover of an Element in a Poset

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6 sample questions

Question 1.
Define a maximal element in a poset.
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Think about elements without any covers above them.
Question 2.
Illustrate what a minimal element looks like in a Hasse diagram.
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Identify where there are no elements below.
3Question 3.
What defines a maximal element in a poset?
- It is less than elements
- It is equal to another element
- No element is related above it
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Think about elements that are at the top.
4Question 4.
True or False: A poset can have multiple maximal elements.
- True
- False
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Consider an example with multiple elements.
Question 5.
Given a poset defined by the relations: A < B, A < C, B < D, C < D, determine all maximal and minimal elements.
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Look for elements not less than or not greater than others.
Question 6.
Construct a poset with elements 1, 2, 3 where 1 < 2 and 1 < 3, and illustrate a Hasse diagram for this.
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Draw the relationships based on the order given.

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