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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define a partition of the set {1, 2, 3, 4}.
💡 Hint: Ensure subsets do not overlap.
Question 2
Easy
What does reflexivity mean in the context of equivalence relations?
💡 Hint: Think of how this applies to any set.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
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
💡 Hint: Consider the properties of subsets in your definition.
Question 2
True or False: Every equivalence relation's equivalence classes can form a partition.
- True
- False
💡 Hint: Recall what defines a valid partition.
Solve 2 more questions and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given the set {x, y, z, a, b}, define a partition and illustrate its equivalence classes.
💡 Hint: Be sure to show how elements relate within these classes demonstrating non-overlapping subsets.
Question 2
Construct an equivalence relation from the partition {{1, 3}, {2, 4}} and prove it is reflexive, symmetric, and transitive.
💡 Hint: Carefully outline each property while validating your relationships.
Challenge and get performance evaluation