Practice - Example with Subset Construction
Enroll to start learning
You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.
Practice Questions
Test your understanding with targeted questions
Define what a partition is in your own words.
💡 Hint: Think about how subsets relate to the whole set.
List the three conditions for a valid partition.
💡 Hint: Recall the definitions we discussed.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What must be true for subsets in a partition of a set?
💡 Hint: Recall the definition of partitioning.
True or False: The equivalence classes formed from an equivalence relation can overlap.
💡 Hint: Think about what it means for classes to be equivalent.
2 more questions available
Challenge Problems
Push your limits with advanced challenges
Given the set S = {a, b, c, d, e} and the partition {{a, b}, {c, d}, {e}}, construct an equivalence relation and justify why it meets the criteria for reflexivity, symmetry, and transitivity.
💡 Hint: Focus first on proving one property of equivalence at a time.
In a university, students are classified into departments: {Math, Science}, {Arts}, and {Engineering}. Create a practical example showing a partition into departments and derive its corresponding equivalence relation.
💡 Hint: Think about how you can link students to different departments for clarification.
Get performance evaluation
Reference links
Supplementary resources to enhance your learning experience.