Practice Anti-symmetric Relation (1.2.4) - Relations and Functions - ICSE 12 Mathematics

Practice: Anti-symmetric Relation

Lesson 1.2.4Relations and Functions

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9 questions

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6 sample questions

Question 1.
Define an anti-symmetric relation.
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Think of the conditions that must be satisfied for a relation to be anti-symmetric.
Question 2.
Provide an example of an anti-symmetric relation.
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Ensure the pairs do not contradict the anti-symmetric property.
3Question 3.
What is an anti-symmetric relation?
- A relation where a = b
- A relation that is both symmetric and reflexive
- A relation where if (a, b) and (b, a) are in R, then a must equal b
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Focus on what conditions need to be met for a relation to be classified as anti-symmetric.
4Question 4.
True or False: The relation R = {(1, 2), (2, 1)} is anti-symmetric.
- True
- False
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Think about the definitions and what they imply about the relationship between the elements.
Question 5.
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.
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Ensure you connect pairs such that the anti-symmetric property remains intact throughout.
Question 6.
Given two anti-symmetric relations R1 and R2 on the same set, what can you conclude about the union of R1 and R2?
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Examine what conditions still need to hold to maintain the anti-symmetric property.

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