Practice Properties Of Equivalence Relations (21.3)

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6 sample questions

Question 1.
What are the three properties of an equivalence relation?
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Use the acronym RST.
Question 2.
Is the relation R defined as (a, b) such that a = b an equivalence relation?
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Consider if each property holds true.
3Question 3.
Which of the following is NOT a property of equivalence relations?
- Reflexive
- Irreflexive
- Symmetric
- Transitive
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Recall the properties we discussed.
4Question 4.
True or False: An equivalence class can be empty.
- True
- False
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Think about how classes are formed based on relations.
Question 5.
Show that the relation R on the set of all people where a R b if they are the same age is an equivalence relation.
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Check each property carefully.
Question 6.
Given the equivalence relation defined by modular arithmetic, form and describe equivalence classes for five distinct integers under modulo 5.
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Picture how numbers relate to the modulus.

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