Practice Introduction (22.2) - Lecture -22 - Discrete Mathematics - Vol 1
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Introduction

Practice - Introduction

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Learning

Practice Questions

Test your understanding with targeted questions

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.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

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.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

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.

Challenge 2 Hard

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.

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