Practice Definitions And Examples (24.1.1) - Cover of an Element in a Poset - part B

Practice: Definitions and Examples

Lesson 24.1.1Cover of an Element in a Poset - part B

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6 sample questions

Question 1.
Define what a cover is in a poset.
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Consider the relationship without anything in between.
Question 2.
What distinguishes a maximal element in a poset?
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Think about what you cannot find above.
3Question 3.
What defines a cover in a poset?
- A direct relationship with an intermediate
- A direct relationship without intermediate
- An unrelated element
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Think about the absence of anything in between.
4Question 4.
True or False: All posets must have both a maximal and a minimal element.
- True
- False
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Consider cases with one element.
Question 5.
In a poset where the elements are the set of all divisors of 12, identify the maximal, minimal, greatest, and least elements.
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Consider how divisors relate to each other and find the topmost and bottommost elements.
Question 6.
Construct a Hasse diagram for the set {a, b, c} with the relationships a < b, a < c. Identify any covers and describe maximal/minimal elements.
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Think about how to organize the elements visually to find relationships.

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