Practice Properties Of Posets And Total Ordering (1.5) - Introduction to Tutorial 4: Part I

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6 sample questions

Question 1.
Define an equivalence relation.
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Consider the properties RST.
Question 2.
Provide an example of a reflexive relation.
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Think of situations where self-identity holds.
3Question 3.
What defines an equivalence relation?
- Reflexive only
- Reflexive
- Symmetric
- Transitive
- Symmetric only
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Recall the RST properties.
4Question 4.
Is the intersection of two equivalence relations an equivalence relation?
- True
- False
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Consider reflexivity, symmetry, and transitivity.
Question 5.
Given a set of five books with different genres, describe how you would establish an equivalence relation based on genre. Discuss if the union of two such relations would still retain properties.
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Consider comparing relations across different categories.
Question 6.
Construct a poset for a collection of shapes based on area and describe its total order. Are there specific comparisons missing?
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Reflect on shapes' relative sizes while visualizing them.

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