Practice Relationship Between Equivalence Relations And Partitions (22.4)

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6 sample questions

Question 1.
Define a partition of the set C = {1, 2, 3, 4}.
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Remember that a partition includes disjoint sets covering the entire set.
Question 2.
What are the properties of an equivalence relation?
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Use the acronym RST as a memory aid.
3Question 3.
What is a key property of a partition?
- All subsets must overlap.
- Each subset must be non-empty and disjoint.
- Subsets can be empty.
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Recall the definition of a partition we discussed.
4Question 4.
If two equivalence classes intersect, what can we conclude?
- True
- False
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Think about the definition of equivalence classes.
Question 5.
Prove that if the equivalence relation R has classes of size 1, then R is trivial.
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Consider what it means for elements to be only related to themselves.
Question 6.
For the set {1, 2, 3, 4, 5}, can you create at least three distinct partitions and describe the equivalence relation for each?
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Focus on how elements belong to each class based on your subsets.

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