Practice - Proof of Properties of Equivalence Relation
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Practice Questions
Test your understanding with targeted questions
Define a partition of the set {a, b, c, d}.
💡 Hint: Make sure the subsets do not overlap.
What does it mean for two subsets to be pairwise disjoint?
💡 Hint: Consider the definition of disjoint sets.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is an equivalence relation?
💡 Hint: Think about the definitions you've learned.
True or False: Every partition of a set results in overlapping subsets.
💡 Hint: Recall the definition of a partition.
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Challenge Problems
Push your limits with advanced challenges
Given a set C with five distinct elements, explore how many different partitions can be formed. Provide your reasoning.
💡 Hint: Consider small cases first to build understanding.
Formulate an equivalence class relation from the set of natural numbers N which relays elements by their parity. Prove it is an equivalence relation.
💡 Hint: Check if the definitions hold according to the properties of equivalence relations.
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Reference links
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