Practice - Part A: Symmetric, Anti-Symmetric and Reflexive Relations
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Practice Questions
Test your understanding with targeted questions
Provide an example of a symmetric relation.
💡 Hint: Think of relationships where mutual conditions apply.
Define a reflexive relation.
💡 Hint: What condition must always hold true in a reflexive relation?
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Interactive Quizzes
Quick quizzes to reinforce your learning
What defines a symmetric relation?
💡 Hint: Think about relations that require mutual connections.
True or False: An anti-symmetric relation can have (a, b) and (b, a) both present if a does not equal b.
💡 Hint: Remember the definition of anti-symmetry.
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Challenge Problems
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Construct a relation on 4 elements that is symmetric yet not reflexive. Describe your relation.
💡 Hint: What must you include while maintaining symmetry and excluding reflexivity?
Prove that any reflexive relation on a set is not anti-symmetric if it includes all pairs.
💡 Hint: Look closely at the definitions and what full inclusion means.
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