Practice Proof Of Properties Of Equivalence Relation (22.5)

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6 sample questions

Question 1.
Define a partition of the set {a, b, c, d}.
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Make sure the subsets do not overlap.
Question 2.
What does it mean for two subsets to be pairwise disjoint?
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Consider the definition of disjoint sets.
3Question 3.
What is an equivalence relation?
- A relation that is only reflexive
- A relation that is symmetric and transitive
- A relation that is reflexive
- symmetric
- and transitive
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Think about the definitions you've learned.
4Question 4.
True or False: Every partition of a set results in overlapping subsets.
- True
- False
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Recall the definition of a partition.
Question 5.
Given a set C with five distinct elements, explore how many different partitions can be formed. Provide your reasoning.
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Consider small cases first to build understanding.
Question 6.
Formulate an equivalence class relation from the set of natural numbers N which relays elements by their parity. Prove it is an equivalence relation.
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Check if the definitions hold according to the properties of equivalence relations.

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