Practice - Question 2: Union and Composition of Equivalence Relations
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Practice Questions
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Define an equivalence relation.
💡 Hint: Think about each property individually.
What is the result of the union of two equivalence relations?
💡 Hint: Consider how pairs combine.
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Interactive Quizzes
Quick quizzes to reinforce your learning
Is the union of two equivalence relations always an equivalence relation?
💡 Hint: Think of specific pairs that could violate this.
What property must hold for R1 ∪ R2 to be an equivalence relation?
💡 Hint: Consider how both relations interact.
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Challenge Problems
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Prove the statement: If R1 is a subset of R2 and both are equivalence relations, what can you say about R1 ∪ R2 and R2?
💡 Hint: Consider subset relationships.
Construct two equivalence relations R1 and R2, where the union is not transitive. Provide elements that demonstrate this.
💡 Hint: Identify ordered pairs that fail to connect transitive links.
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