Practice - Examples of Equivalence Classes
Enroll to start learning
You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.
Practice Questions
Test your understanding with targeted questions
What does it mean for a relation to be reflexive?
💡 Hint: Think about a number interacting with itself.
Give an example of an equivalence class in mod 3.
💡 Hint: Consider what results when you divide the integers by 3.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What property states that if a is related to b, then b is also related to a?
💡 Hint: Think about how relationships mirror each other.
True or False: An equivalence class can be empty.
💡 Hint: Recall the property of every equivalence class.
1 more question available
Challenge Problems
Push your limits with advanced challenges
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.
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.
Get performance evaluation
Reference links
Supplementary resources to enhance your learning experience.