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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define an equivalence relation.
💡 Hint: Think about how elements relate to each other.
Question 2
Easy
What is a partition of a set?
💡 Hint: Remember what happens to the original set's elements in a partition.
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 one property an equivalence relation must satisfy?
- A. Only reflexive
- B. Reflexive and transitive
- C. Reflexive
- symmetric
- and transitive
💡 Hint: Remember the three defining properties.
Question 2
True or False? Every equivalence class is empty.
- True
- False
💡 Hint: Consider the definition of equivalence classes.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given a set of numbers S = {1, 2, 3, 4, 5}, define an equivalence relation that groups elements into three classes. Explain how your relation satisfies the three properties.
💡 Hint: Describe the method you use to determine group membership.
Question 2
Construct a partition for the set of letters in the word 'HELLO' and relate it to an equivalence relation.
💡 Hint: Think about how repeated elements influence group formation.
Challenge and get performance evaluation