Practice - Relationship between Equivalence Relations and Partitions
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Practice Questions
Test your understanding with targeted questions
Define a partition of the set C = {1, 2, 3, 4}.
💡 Hint: Remember that a partition includes disjoint sets covering the entire set.
What are the properties of an equivalence relation?
💡 Hint: Use the acronym RST as a memory aid.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is a key property of a partition?
💡 Hint: Recall the definition of a partition we discussed.
If two equivalence classes intersect, what can we conclude?
💡 Hint: Think about the definition of equivalence classes.
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Challenge Problems
Push your limits with advanced challenges
Prove that if the equivalence relation R has classes of size 1, then R is trivial.
💡 Hint: Consider what it means for elements to be only related to themselves.
For the set {1, 2, 3, 4, 5}, can you create at least three distinct partitions and describe the equivalence relation for each?
💡 Hint: Focus on how elements belong to each class based on your subsets.
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