Practice - Symmetry
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Practice Questions
Test your understanding with targeted questions
What is an equivalence relation?
💡 Hint: Think about the properties it needs to satisfy.
Provide a simple example of a partition.
💡 Hint: Make sure the subsets do not share any elements.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the primary property that defines an equivalence relation?
💡 Hint: Consider what each property entails.
True or False: A partition can include empty subsets.
💡 Hint: Think about the definition of a partition.
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Challenge Problems
Push your limits with advanced challenges
If set A = {1, 2, 3} and set B = {3, 4, 5}, create an equivalence relation that relates elements of A to elements of B.
💡 Hint: Consider how you might categorize elements across the two sets.
Given a set S = {x, y, z, w} and the partition {{x, y}, {z, w}}, formulate the equivalence relation and justify its reflexivity, symmetry, and transitivity.
💡 Hint: Revisit how to articulate properties based on pairs.
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