Practice Transitivity (22.5.3) - Lecture -22 - Discrete Mathematics

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6 sample questions

Question 1.
Define a partition of the set {1, 2, 3, 4}.
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Ensure subsets do not overlap.
Question 2.
What does reflexivity mean in the context of equivalence relations?
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Think of how this applies to any set.
3Question 3.
What is a partition of a set?
- A group of overlapping subsets
- Non-empty disjoint subsets whose union is the set
- Only one subset of the whole set
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Consider the properties of subsets in your definition.
4Question 4.
True or False: Every equivalence relation's equivalence classes can form a partition.
- True
- False
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Recall what defines a valid partition.
Question 5.
Given the set {x, y, z, a, b}, define a partition and illustrate its equivalence classes.
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Be sure to show how elements relate within these classes demonstrating non-overlapping subsets.
Question 6.
Construct an equivalence relation from the partition {{1, 3}, {2, 4}} and prove it is reflexive, symmetric, and transitive.
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Carefully outline each property while validating your relationships.

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