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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What does it mean for a relation to be reflexive?
💡 Hint: Think about a number interacting with itself.
Question 2
Easy
Give an example of an equivalence class in mod 3.
💡 Hint: Consider what results when you divide the integers by 3.
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 states that if a is related to b, then b is also related to a?
- Reflexivity
- Symmetry
- Transitivity
💡 Hint: Think about how relationships mirror each other.
Question 2
True or False: An equivalence class can be empty.
- True
- False
💡 Hint: Recall the property of every equivalence class.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given the relation a ≡ b (mod 4), determine whether pairs (6, 10) and (2, 6) belong to the same equivalence class. Justify your answer.
💡 Hint: Check the remainder of each number when divided by 4.
Question 2
Prove that all integers can be classified under an equivalence relation based on their remainders when divided by n for any integer n > 0.
💡 Hint: Utilize a proof by contradiction regarding shared remainders.
Challenge and get performance evaluation