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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the power set of a set {a, b}?
💡 Hint: Remember to list all subsets.
Question 2
Easy
Consider the set A = {x, y}; how many elements are in P(A)?
💡 Hint: Each element can either be included or not included.
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 theorem shows that the cardinality of a set is less than that of its power set?
- Axiom of Choice
- Cantor's Theorem
- Zermelo's theorem
💡 Hint: Think about who originally presented the concept of comparing sizes of infinity.
Question 2
If a set has 5 elements, how many elements does its power set have?
- True
- False
💡 Hint: Remember the formula for calculating the power set.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Consider a set with 4 elements. Prove that there exists no surjective function from this set to its power set.
💡 Hint: Define the function and illustrate the mapping before finding S.
Question 2
If we apply Cantor's theorem repeatedly, what can we say about the cardinality of the power set of the power set of the natural numbers?
💡 Hint: Remember that each application of Cantor's theorem shows distinct infinities.
Challenge and get performance evaluation