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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 the three properties that must be satisfied.
Question 2
Easy
What does it mean to partition a set?
💡 Hint: Consider how groups of elements can be formed.
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 defines an equivalence relation?
- Only reflexive
- Reflexive
- symmetric
- and transitive
- Only symmetric
💡 Hint: Remember the properties we discussed using RST.
Question 2
Does every partition of a set form an equivalence relation?
- True
- False
💡 Hint: Think about how each element is categorized.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given a set with 50 elements, partition this set into four equal subsets and find the number of ordered pairs within each subset.
💡 Hint: Break down the problem by first finding the size of each subset.
Question 2
Prove that if a relation R on a set A is reflexive and symmetric, it does not imply R is transitive. Provide a counterexample.
💡 Hint: Reflect on how pairing can lead to violations of transitivity.
Challenge and get performance evaluation