Practice - Question 1: Equivalence Relations - Part A
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Practice Questions
Test your understanding with targeted questions
What properties must an equivalence relation satisfy?
💡 Hint: Think about the initials 'RST'.
Give an example of a reflexive relation.
💡 Hint: Consider any single element of a set.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is an equivalence relation?
💡 Hint: Recall the three properties we discussed.
True or False: The union of two equivalence relations is always an equivalence relation.
💡 Hint: Think of the counterexamples we discussed.
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Challenge Problems
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Suppose R1 and R2 are two equivalence relations defined on the set {x, y, z}. Describe the union and intersection of these relations and show whether they remain equivalence relations.
💡 Hint: Use specific pairs from both relations to illustrate.
Provide a scenario where the union of two equivalence relations fails transitivity and prove your point with an example.
💡 Hint: Identify which pairs are present and which are missing.
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