Practice - Part B: Symmetric, Anti-Symmetric and Irreflexive Relations
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Practice Questions
Test your understanding with targeted questions
Define a symmetric relation in your own words.
💡 Hint: Think about how relationships often work in pairs.
What is an example of an irreflexive relation?
💡 Hint: Consider numerical comparisons where one number can’t equal itself.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What defines a symmetric relation?
💡 Hint: What would happen if you reversed the pairs in a relationship?
True or False: An anti-symmetric relation can have (a, a) and (b, b) without issue.
💡 Hint: Consider the definition of anti-symmetry carefully.
1 more question available
Challenge Problems
Push your limits with advanced challenges
Given a set A = {a, b, c}, construct all possible relations and categorize them by symmetry, anti-symmetry, and irreflexivity.
💡 Hint: Use the definition of each type to guide your categorization.
Prove that a symmetric relation on a set can never be irreflexive.
💡 Hint: Start with the definitions of symmetric and irreflexive relations.
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