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

Practice - Existence of Maximal and Minimal Elements

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Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

Define a maximal element in a poset with an example.

💡 Hint: Think about the largest number in a small set.

Question 2 Easy

What is a minimal element?

💡 Hint: Consider the smallest number in a sorted list.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

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

💡 Hint: Think of the highest point in a hierarchy.

Question 2

In a poset, can an element be both maximal and minimal?

True
False

💡 Hint: Think about a single point set.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Consider a poset defined by the relationships 1 < 2, 2 < 3, and 1 < 3. Define which elements are maximal, minimal, greatest, and least.

💡 Hint: Draw a Hasse diagram to visualize.

Challenge 2 Hard

Create an example of a poset that has more than one maximal element but no least element.

💡 Hint: Think about relations which do not connect all elements.

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Reference links

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