Practice - Discrete Mathematics
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Practice Questions
Test your understanding with targeted questions
What properties must a relation have to be classified as an equivalence relation?
💡 Hint: Remember the three core properties.
Define the intersection of two relations.
💡 Hint: Think about common elements shared by both relations.
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Interactive Quizzes
Quick quizzes to reinforce your learning
Which of the following must a relation possess to be an equivalence relation?
💡 Hint: Think about the definition of equivalence relations.
True or False: The intersection of two equivalence relations is always an equivalence relation.
💡 Hint: Remember to evaluate the three main properties.
1 more question available
Challenge Problems
Push your limits with advanced challenges
Prove that the union of two equivalence relations cannot form an equivalence relation if their compositions do not hold.
💡 Hint: Refer to the definitions of each property and highlight the failure.
Construct a unique example of two equivalence relations on a set that illustrates both the union being not transitive and intersection being transitive.
💡 Hint: Investigate examples systematically and focus on distinct pairs.
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