Practice Hasse Diagrams And Their Categories (1.4) - Introduction to Tutorial 4: Part I

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6 sample questions

Question 1.
Describe a Hasse diagram with three elements that shows no relationships.
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Think of three separate dots.
Question 2.
What makes a relation a partial order?
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Consider the definitions of these properties.
3Question 3.
What is a Hasse diagram?
- A type of graph for functions
- A way to visualize partially ordered sets
- An equation
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Think of how we visualize elements and their order.
4Question 4.
A relation must be reflexive, antisymmetric, and transitive to be considered a?
- Total order
- Partial order
- Linear chain
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Look at the definitions of the properties.
Question 5.
Construct Hasse diagrams for the set {x, y, z} where x is the least element. Identify the relationships.
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Visualize how many nodes are connected and their direct order.
Question 6.
Prove that a set with n elements can have a maximum of 2^n - 1 distinct Hasse diagrams.
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Consider how many ways you can compare each pair of elements.

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