Practice Counterexamples and Properties of Equivalence Relations - 1.2 | 1. Introduction to Tutorial 4: Part I | Discrete Mathematics - Vol 2
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1.2 - Counterexamples and Properties of Equivalence Relations

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Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

Define reflexivity in the context of equivalence relations.

💡 Hint: Think of how each element compares to itself.

Question 2

Easy

Is the union of two equivalence relations always reflexive? Why or why not?

💡 Hint: Consider what reflexivity requires.

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

What are the three properties required for a relation to be classified as an equivalence relation?

  • Reflexivity
  • symmetry
  • transitivity
  • Reflexivity
  • antisymmetry
  • symmetry
  • Symmetry
  • transitivity
  • antisymmetry

💡 Hint: Recall the definitions of each property.

Question 2

True or False: The union of two equivalence relations is always an equivalence relation.

  • True
  • False

💡 Hint: Think about counterexamples demonstrating transitivity issues.

Solve 2 more questions and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

Define equivalence relations and provide a real-world scenario where such relations apply. Then analyze if the union of the scenarios forms an equivalence relation.

💡 Hint: Explore connections through examples relevant to education or social classes.

Question 2

Create a recursive structure to count equivalence relations on a set of 4 elements, P(4), using the provided function P(n).

💡 Hint: Break down into selected subsets and analyze how remaining elements are partitioned.

Challenge and get performance evaluation