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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define cardinality.
💡 Hint: Think about how we count items in a group.
Question 2
Easy
What is a power set?
💡 Hint: Recall how subsets can form from the original 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 does Cantor's theorem state about set A and its power set P(A)?
- |A| = |P(A)|
- |A| < |P(A)|
- |A| > |P(A)|
💡 Hint: Reflect on the relationship between a set and its subsets.
Question 2
Is the following statement true or false? 'The power set of a countably infinite set is also countably infinite.'
- True
- False
💡 Hint: Think about how many subsets can be formed from infinite sets.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Create a set A with 3 elements and list all its subsets. Discuss the cardinality of A and P(A).
💡 Hint: Count both the set and its subsets carefully.
Question 2
Discuss the implications of Cantor's theorem using a real-world analogy or its effects on mathematical theory.
💡 Hint: Reflect on how understanding different infinities affects both math and science.
Challenge and get performance evaluation