Practice Implication Of Equivalence Classes (21.7)

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6 sample questions

Question 1.
What are the three properties that define an equivalence relation?
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Remember the acronym RST.
Question 2.
Give an example of a reflexive relation.
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Think of numbers.
3Question 3.
Which of the following are properties of equivalence relations?
- Reflexive
- Transitive
- Both A and B
- None
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RST is key!
4Question 4.
True or False: Equivalence classes can share elements with each other.
- True
- False
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Think about the definition.
Question 5.
Demonstrate how to prove that every equivalence class under a given relation is non-empty.
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Start from the definition of an equivalence relation.
Question 6.
Given that [0] and [3] represent two equivalence classes under modulo 3, prove whether they share elements or not.
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Consider their definitions carefully.

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