Practice - Question 7: Equivalence Relation
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Practice Questions
Test your understanding with targeted questions
Define an equivalence relation.
💡 Hint: Think about the three properties that must be satisfied.
What does it mean to partition a set?
💡 Hint: Consider how groups of elements can be formed.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What defines an equivalence relation?
💡 Hint: Remember the properties we discussed using RST.
Does every partition of a set form an equivalence relation?
💡 Hint: Think about how each element is categorized.
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Challenge Problems
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Given a set with 50 elements, partition this set into four equal subsets and find the number of ordered pairs within each subset.
💡 Hint: Break down the problem by first finding the size of each subset.
Prove that if a relation R on a set A is reflexive and symmetric, it does not imply R is transitive. Provide a counterexample.
💡 Hint: Reflect on how pairing can lead to violations of transitivity.
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