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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define a partition of the set C = {1, 2, 3, 4}.
💡 Hint: Remember that a partition includes disjoint sets covering the entire set.
Question 2
Easy
What are the properties of an equivalence relation?
💡 Hint: Use the acronym RST as a memory aid.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What is a key property of a partition?
- All subsets must overlap.
- Each subset must be non-empty and disjoint.
- Subsets can be empty.
💡 Hint: Recall the definition of a partition we discussed.
Question 2
If two equivalence classes intersect, what can we conclude?
- True
- False
💡 Hint: Think about the definition of equivalence classes.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
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.
Question 2
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.
Challenge and get performance evaluation