Practice - Transitivity
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Practice Questions
Test your understanding with targeted questions
Define a partition of the set {1, 2, 3, 4}.
💡 Hint: Ensure subsets do not overlap.
What does reflexivity mean in the context of equivalence relations?
💡 Hint: Think of how this applies to any set.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is a partition of a set?
💡 Hint: Consider the properties of subsets in your definition.
True or False: Every equivalence relation's equivalence classes can form a partition.
💡 Hint: Recall what defines a valid partition.
2 more questions available
Challenge Problems
Push your limits with advanced challenges
Given the set {x, y, z, a, b}, define a partition and illustrate its equivalence classes.
💡 Hint: Be sure to show how elements relate within these classes demonstrating non-overlapping subsets.
Construct an equivalence relation from the partition {{1, 3}, {2, 4}} and prove it is reflexive, symmetric, and transitive.
💡 Hint: Carefully outline each property while validating your relationships.
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