Practice Equivalence Relation (21) - Equivalence Relation - Discrete Mathematics

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6 sample questions

Question 1.
What are the three properties that define an equivalence relation?
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Think of the acronym RST.
Question 2.
Provide an example of an equivalence relation on the set of integers.
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Consider how integers can relate based on remainders.
3Question 3.
What property states that every element is related to itself?
- Reflexive
- Symmetric
- Transitive
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It's one of the RST properties.
4Question 4.
True or False: All elements in an equivalence class must be related to at least one other element.
- True
- False
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Consider the definition of an equivalence class.
Question 5.
Prove that the relation defined as (a, b) if a - b is divisible by 7 is an equivalence relation.
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Assume a, b, c are any integers and verify each property.
Question 6.
Consider a set of students where two students are equivalent if they are in the same year. Explain whether this defines an equivalence relation.
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Sketch out each property to clarify the relationships.

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