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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What properties must a relation have to be classified as an equivalence relation?
💡 Hint: Remember the three core properties.
Question 2
Easy
Define the intersection of two relations.
💡 Hint: Think about common elements shared by both relations.
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
Which of the following must a relation possess to be an equivalence relation?
- Reflexive
- Associative
- Symmetric
💡 Hint: Think about the definition of equivalence relations.
Question 2
True or False: The intersection of two equivalence relations is always an equivalence relation.
- True
- False
💡 Hint: Remember to evaluate the three main properties.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Prove that the union of two equivalence relations cannot form an equivalence relation if their compositions do not hold.
💡 Hint: Refer to the definitions of each property and highlight the failure.
Question 2
Construct a unique example of two equivalence relations on a set that illustrates both the union being not transitive and intersection being transitive.
💡 Hint: Investigate examples systematically and focus on distinct pairs.
Challenge and get performance evaluation