Practice - Introduction
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Practice Questions
Test your understanding with targeted questions
Define an equivalence relation. List its three properties.
💡 Hint: Think of properties that a relation must hold for elements to be considered equivalent.
What is a partition? Give a real-world example.
💡 Hint: Consider how objects can be grouped without overlaps.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What are the three properties of an equivalence relation?
💡 Hint: Remember the definitions of each property.
True or False: A partition can have overlapping subsets.
💡 Hint: Think about how subsets in a partition interact with each other.
1 more question available
Challenge Problems
Push your limits with advanced challenges
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.
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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