Practice Introduction To Tutorial 4: Part I (1.1.1) - Introduction to Tutorial 4: Part I

Practice: Introduction to Tutorial 4: Part I

Lesson 1.1.1Introduction to Tutorial 4: Part I

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9 questions

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6 sample questions

Question 1.
List the three properties of equivalence relations.
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Think about what it means for a relation to be an equivalence.
Question 2.
True or False? The union of two equivalence relations is always an equivalence relation.
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Consider if the union could ever lose transitivity.
3Question 3.
What are the three properties required for a relation to be an equivalence relation?
- Reflexivity
- Symmetry
- Transitivity
- Completeness
- Reflexivity
- Antisymmetry
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Think about the definitions we've discussed.
4Question 4.
True or False? The intersection of two equivalence relations is always an equivalence relation.
- True
- False
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Consider how the properties overlap.
Question 5.
Define a custom set and create two distinct equivalence relations on it. Analyze and demonstrate their union and intersection.
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Work through constructing the relations step by step.
Question 6.
Prove that the union of two equivalence relations forms a new relation that does not alter the existing reflexive pairs.
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Check the properties of union through individual reflexive elements.

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