Practice Equivalence Classes (21.4) - Equivalence Relation - Discrete Mathematics - Vol 1
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Equivalence Classes

Practice - Equivalence Classes

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Practice Questions

Test your understanding with targeted questions

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.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

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.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

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.

Challenge 2 Hard

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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