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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 each property individually.
Question 2
Easy
What is the result of the union of two equivalence relations?
💡 Hint: Consider how pairs combine.
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
Is the union of two equivalence relations always an equivalence relation?
- True
- False
💡 Hint: Think of specific pairs that could violate this.
Question 2
What property must hold for R1 ∪ R2 to be an equivalence relation?
- It must be reflexive
- It must be symmetric
- R1 ∘ R2 = R1 ∪ R2
- Both A and B
💡 Hint: Consider how both relations interact.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Prove the statement: If R1 is a subset of R2 and both are equivalence relations, what can you say about R1 ∪ R2 and R2?
💡 Hint: Consider subset relationships.
Question 2
Construct two equivalence relations R1 and R2, where the union is not transitive. Provide elements that demonstrate this.
💡 Hint: Identify ordered pairs that fail to connect transitive links.
Challenge and get performance evaluation