Practice - Equivalence Classes
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Practice Questions
Test your understanding with targeted questions
What does it mean for a relation to be reflexive?
💡 Hint: Think about how elements relate to themselves.
List one property of equivalence relations.
💡 Hint: Recall the three key properties.
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Interactive Quizzes
Quick quizzes to reinforce your learning
Which property is NOT required for a relation to be an equivalence relation?
💡 Hint: Think about the definitions of these properties.
True or False: Two equivalence classes can share some elements.
💡 Hint: Recall the property of equivalence classes regarding their separation.
1 more question available
Challenge Problems
Push your limits with advanced challenges
Given the set of integers Z and the relation defined by modulo 5, calculate and list all equivalence classes.
💡 Hint: Consider what numbers share the same remainder when divided by 5.
Prove or disprove: There exists integers a and b such that a ≡ b (mod m) but a is not equal to b.
💡 Hint: Look at how properties of congruence work under different moduli.
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