Practice Disjoint Equivalence Classes (21.6) - Equivalence Relation - Discrete Mathematics

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6 sample questions

Question 1.
What are the three properties of an equivalence relation?
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Think about how elements relate to themselves and each other.
Question 2.
What does it mean for two sets to be disjoint?
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Consider how they can exist with no overlap.
3Question 3.
What property guarantees that every element is related to itself?
- Symmetry
- Reflexivity
- Transitivity
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Think of the 'self' aspect of a relation.
4Question 4.
True or False: Equivalence classes can share some common elements.
- True
- False
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Consider the definitions of equivalence classes.
Question 5.
Prove that under any equivalence relation, the union of equivalence classes covers the entire set A.
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Consider every element's relation to itself.
Question 6.
Given an equivalence relation defined on a set of integers, show that any integer belongs to only one equivalence class.
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Examine how equivalence classes link back to remainders.

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