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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is an equivalence relation?
💡 Hint: Think about the properties it needs to satisfy.
Question 2
Easy
Provide a simple example of a partition.
💡 Hint: Make sure the subsets do not share any elements.
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 the primary property that defines an equivalence relation?
- Only reflexivity
- All three properties: Reflexivity
- Symmetry
- Transitivity
- Only symmetry
💡 Hint: Consider what each property entails.
Question 2
True or False: A partition can include empty subsets.
- True
- False
💡 Hint: Think about the definition of a partition.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
If set A = {1, 2, 3} and set B = {3, 4, 5}, create an equivalence relation that relates elements of A to elements of B.
💡 Hint: Consider how you might categorize elements across the two sets.
Question 2
Given a set S = {x, y, z, w} and the partition {{x, y}, {z, w}}, formulate the equivalence relation and justify its reflexivity, symmetry, and transitivity.
💡 Hint: Revisit how to articulate properties based on pairs.
Challenge and get performance evaluation