Practice From Partition To Equivalence Relation (22.4.2)

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10 questions

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3 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
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Quiz
4 questions · about 3 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
Define a partition in your own words.
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Focus on the key terms non-empty, disjoint, and covering.
Question 2.
Give an example of a simple partition from everyday life.
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Think of how people can be categorized based on shared attributes.
3Question 3.
What are the three properties of an equivalence relation?
- Reflexive
- Symmetric
- Transitive
- Only Reflexive
- Non-empty
- Overlapping-free
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Revise the definitions of the properties.
4Question 4.
True or False: A partition can have subsets that overlap.
- True
- False
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Consider what it means for subsets to be a partition.
Question 5.
Given a set of students, partition them based on their grade levels and define the corresponding equivalence relation.
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Consider how students in the same grade relate.
Question 6.
Create a non-trivial partition of the set {1,2,3,4,5,6}, determine the equivalence relation, and verify that all properties hold.
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Focus on pair combinations from each subset.

6 more questions in this section. Enroll free to practise them all.