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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define an equivalence relation.
💡 Hint: What are the three key properties?
Question 2
Easy
Is the union of two reflexive relations always reflexive?
💡 Hint: What does reflexivity require?
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 property does the union of two equivalence relations always maintain?
- Reflexivity
- Transitivity
- Antisymmetry
💡 Hint: Consider what it means for a relation to be reflexive.
Question 2
True or False: The intersection of two equivalence relations is always an equivalence relation.
- True
- False
💡 Hint: Review the conditions of equivalence relations.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Create an example of two equivalence relations where their union is not an equivalence relation, and specify the failure of transitivity.
💡 Hint: Remember to check the interconnectedness of the elements when forming unions.
Question 2
Prove using contradiction that if the union of two equivalence relations isn't symmetric, then at least one of them isn't an equivalence relation.
💡 Hint: Focus on how each relation interconnects and what requires them to succeed.
Challenge and get performance evaluation