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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What properties must an equivalence relation satisfy?
💡 Hint: Think about the initials 'RST'.
Question 2
Easy
Give an example of a reflexive relation.
💡 Hint: Consider any single element of a set.
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 an equivalence relation?
- Only reflexive
- Reflexive
- symmetric
- and transitive
- None of the above
💡 Hint: Recall the three properties we discussed.
Question 2
True or False: The union of two equivalence relations is always an equivalence relation.
- True
- False
💡 Hint: Think of the counterexamples we discussed.
Solve 2 more questions and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Suppose R1 and R2 are two equivalence relations defined on the set {x, y, z}. Describe the union and intersection of these relations and show whether they remain equivalence relations.
💡 Hint: Use specific pairs from both relations to illustrate.
Question 2
Provide a scenario where the union of two equivalence relations fails transitivity and prove your point with an example.
💡 Hint: Identify which pairs are present and which are missing.
Challenge and get performance evaluation