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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Provide an example of a symmetric relation.
💡 Hint: Think of relationships where mutual conditions apply.
Question 2
Easy
Define a reflexive relation.
💡 Hint: What condition must always hold true in a reflexive relation?
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What defines a symmetric relation?
- If (a
- b) implies (b
- a)
- If (a
- b) implies (a
- c)
- If no elements relate to themselves
💡 Hint: Think about relations that require mutual connections.
Question 2
True or False: An anti-symmetric relation can have (a, b) and (b, a) both present if a does not equal b.
- True
- False
💡 Hint: Remember the definition of anti-symmetry.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
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?
Question 2
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.
Challenge and get performance evaluation