Practice Question 1: Equivalence Relations - Part A (1.1.2)

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6 sample questions

Question 1.
What properties must an equivalence relation satisfy?
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Think about the initials 'RST'.
Question 2.
Give an example of a reflexive relation.
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Consider any single element of a set.
3Question 3.
What is an equivalence relation?
- Only reflexive
- Reflexive
- symmetric
- and transitive
- None of the above
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Recall the three properties we discussed.
4Question 4.
True or False: The union of two equivalence relations is always an equivalence relation.
- True
- False
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Think of the counterexamples we discussed.
Question 5.
Suppose R1 and R2 are two equivalence relations defined on the set {x, y, z}. Describe the union and intersection of these relations and show whether they remain equivalence relations.
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Use specific pairs from both relations to illustrate.
Question 6.
Provide a scenario where the union of two equivalence relations fails transitivity and prove your point with an example.
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Identify which pairs are present and which are missing.

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