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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 how elements relate to themselves.
Question 2
Easy
List one property of equivalence relations.
💡 Hint: Recall the three key properties.
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
Which property is NOT required for a relation to be an equivalence relation?
- Transitivity
- Symmetry
- Asymmetry
💡 Hint: Think about the definitions of these properties.
Question 2
True or False: Two equivalence classes can share some elements.
- True
- False
💡 Hint: Recall the property of equivalence classes regarding their separation.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
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.
Question 2
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.
Challenge and get performance evaluation