Practice Existence Of Maximal And Minimal Elements (24.2.3) - Cover of an Element in a Poset

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6 sample questions

Question 1.
Define a maximal element in a poset with an example.
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Think about the largest number in a small set.
Question 2.
What is a minimal element?
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Consider the smallest number in a sorted list.
3Question 3.
What is a maximal element in a poset?
- An element that is less than others
- An element that cannot have elements above it
- An element with no relations
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Think of the highest point in a hierarchy.
4Question 4.
In a poset, can an element be both maximal and minimal?
- True
- False
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Think about a single point set.
Question 5.
Consider a poset defined by the relationships 1 < 2, 2 < 3, and 1 < 3. Define which elements are maximal, minimal, greatest, and least.
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Draw a Hasse diagram to visualize.
Question 6.
Create an example of a poset that has more than one maximal element but no least element.
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Think about relations which do not connect all elements.

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