Practice Introduction - 22.2 | 22. Lecture -22 | Discrete Mathematics - Vol 1
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22.2 - Introduction

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Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

Define an equivalence relation. List its three properties.

💡 Hint: Think of properties that a relation must hold for elements to be considered equivalent.

Question 2

Easy

What is a partition? Give a real-world example.

💡 Hint: Consider how objects can be grouped without overlaps.

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 of an equivalence relation?

  • Reflexivity
  • Disjointness
  • Transitivity
  • Reflexivity
  • Symmetry
  • Transitivity
  • Symmetry
  • Pairwise
  • Union

💡 Hint: Remember the definitions of each property.

Question 2

True or False: A partition can have overlapping subsets.

  • True
  • False

💡 Hint: Think about how subsets in a partition interact with each other.

Solve 1 more question and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

Take the set {3, 5, 7, 9} and define a relation that is an equivalence relation. Prove it is reflexive, symmetric, and transitive.

💡 Hint: Focus on the definitions of the properties and how they apply to odd numbers.

Question 2

Given a set of animals [Dog, Cat, Cow] and their classification [Mammal, Reptile], form partitions based on their classifications. Explain the equivalence relation established.

💡 Hint: Think about how animals relate to classifications and how this forms an equivalence.

Challenge and get performance evaluation