1.2.4 - Anti-symmetric Relation
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Practice Questions
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Define an anti-symmetric relation.
💡 Hint: Think of the conditions that must be satisfied for a relation to be anti-symmetric.
Provide an example of an anti-symmetric relation.
💡 Hint: Ensure the pairs do not contradict the anti-symmetric property.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is an anti-symmetric relation?
💡 Hint: Focus on what conditions need to be met for a relation to be classified as anti-symmetric.
True or False: The relation R = {(1, 2), (2, 1)} is anti-symmetric.
💡 Hint: Think about the definitions and what they imply about the relationship between the elements.
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Challenge Problems
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Create a new relation on set A = {1, 2, 3, 4} that is anti-symmetric and contains at least five ordered pairs. Explain your choice.
💡 Hint: Ensure you connect pairs such that the anti-symmetric property remains intact throughout.
Given two anti-symmetric relations R1 and R2 on the same set, what can you conclude about the union of R1 and R2?
💡 Hint: Examine what conditions still need to hold to maintain the anti-symmetric property.
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