Practice Functions And Partitions (1.3) - Introduction to Tutorial 4: Part I

Practice: Functions and Partitions

Lesson 1.3Introduction to Tutorial 4: Part I

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6 sample questions

Question 1.
Define an equivalence relation.
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What are the three key properties?
Question 2.
Is the union of two reflexive relations always reflexive?
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What does reflexivity require?
3Question 3.
What property does the union of two equivalence relations always maintain?
- Reflexivity
- Transitivity
- Antisymmetry
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Consider what it means for a relation to be reflexive.
4Question 4.
True or False: The intersection of two equivalence relations is always an equivalence relation.
- True
- False
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Review the conditions of equivalence relations.
Question 5.
Create an example of two equivalence relations where their union is not an equivalence relation, and specify the failure of transitivity.
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Remember to check the interconnectedness of the elements when forming unions.
Question 6.
Prove using contradiction that if the union of two equivalence relations isn't symmetric, then at least one of them isn't an equivalence relation.
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Focus on how each relation interconnects and what requires them to succeed.

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