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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 \{1, 2, 3, 4\}.
💡 Hint: Make sure to include non-empty disjoint subsets.
Question 2
Easy
True or False: In a partition, two subsets can overlap.
💡 Hint: Remember the definition of disjoint subsets.
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 defines an equivalence relation?
- Reflexive
- symbiotic
- Reflexive
- symmetric
- transitive
- Asymmetric and cyclic
💡 Hint: Think about the properties you learned.
Question 2
True or False: A partition can contain empty subsets.
- True
- False
💡 Hint: Refer to the definition of partitions.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given the set \( C = \{a, b, c, d, e, f\} \) and the partition \( P = \{\{a, b\}, \{c, d, e\}, \{f\}\}, \) construct the equivalence relation and prove its properties.
💡 Hint: Check the conditions for creating pairs from subsets within the partition.
Question 2
Determine the number of possible partitions for the set \( \{1, 2, 3, 4\} \).
💡 Hint: Think about all the ways to combine and split into disjoint non-empty subsets.
Challenge and get performance evaluation