Practice Greatest And Least Elements In A Poset (24.3) - Cover of an Element in a Poset - part B

Practice: Greatest and Least Elements in a Poset

Lesson 24.3Cover of an Element in a Poset - part B

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9 questions

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4 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
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3 questions · about 2 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
What is a poset? Provide a simple definition.
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Think about the properties of the ordering.
Question 2.
Can you give an example of a minimal element in a simple poset?
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Identify the element with no lower relations.
3Question 3.
What defines a cover in a poset?
- It is any two elements
- It is an element that has the properties of maximal elements
- It indicates a direct relationship without any intermediary.
- It must be a numerical less than.
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Think of the visual representation.
4Question 4.
True or False: A poset can have multiple greatest elements.
- True
- False
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Consider the definition of a greatest element.
Question 5.
Create a Hasse diagram for a poset defined as follows: {1, 2, 3, 4} with relations 1 < 2, 1 < 3, 2 < 4, and state which elements are maximal and minimal.
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Sketch the relations and see how they connect visually.
Question 6.
Illustrate a poset with at least one greatest, one least, and multiple minimal and maximal elements, then explain their significance.
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Consider how many ways elements relate to one another.

5 more questions in this section. Enroll free to practise them all.