Practice - Equivalence Relation
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Practice Questions
Test your understanding with targeted questions
What are the three properties that define an equivalence relation?
💡 Hint: Think of the acronym RST.
Provide an example of an equivalence relation on the set of integers.
💡 Hint: Consider how integers can relate based on remainders.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What property states that every element is related to itself?
💡 Hint: It's one of the RST properties.
True or False: All elements in an equivalence class must be related to at least one other element.
💡 Hint: Consider the definition of an equivalence class.
1 more question available
Challenge Problems
Push your limits with advanced challenges
Prove that the relation defined as (a, b) if a - b is divisible by 7 is an equivalence relation.
💡 Hint: Assume a, b, c are any integers and verify each property.
Consider a set of students where two students are equivalent if they are in the same year. Explain whether this defines an equivalence relation.
💡 Hint: Sketch out each property to clarify the relationships.
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