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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define what a partition is in your own words.
💡 Hint: Think about how subsets relate to the whole set.
Question 2
Easy
List the three conditions for a valid partition.
💡 Hint: Recall the definitions we discussed.
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 must be true for subsets in a partition of a set?
- They must be overlapping.
- They must cover the original set.
- They can be empty.
💡 Hint: Recall the definition of partitioning.
Question 2
True or False: The equivalence classes formed from an equivalence relation can overlap.
- True
- False
💡 Hint: Think about what it means for classes to be equivalent.
Solve 2 more questions and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given the set S = {a, b, c, d, e} and the partition {{a, b}, {c, d}, {e}}, construct an equivalence relation and justify why it meets the criteria for reflexivity, symmetry, and transitivity.
💡 Hint: Focus first on proving one property of equivalence at a time.
Question 2
In a university, students are classified into departments: {Math, Science}, {Arts}, and {Engineering}. Create a practical example showing a partition into departments and derive its corresponding equivalence relation.
💡 Hint: Think about how you can link students to different departments for clarification.
Challenge and get performance evaluation