Practice Theorem On Equivalence Classes (21.8) - Equivalence Relation - Discrete Mathematics - Vol 1
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Theorem on Equivalence Classes

Practice - Theorem on Equivalence Classes

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Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What are the three properties of an equivalence relation?

💡 Hint: Think of the acronym RST.

Question 2 Easy

Is (2, 2) in a relation R considered reflexive?

💡 Hint: Check if it holds true for any a.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What property requires that an element be related to itself in an equivalence relation?

Symmetric
Transitive
Reflexive

💡 Hint: Think of 'self-relationship'.

Question 2

True or False: In an equivalence relation, if a is related to b, then b must be related to a.

True
False

💡 Hint: Remember the 'back and forth' characteristic.

2 more questions available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Given a set of integers and a relation defined as a ≡ b (mod 5), classify the integers based on their equivalence classes.

💡 Hint: Consider the remainders when each integer is divided by 5.

Challenge 2 Hard

Prove that if two equivalence classes have any element in common, they are the same class.

💡 Hint: Think about how elements are classified in equivalence relations.

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