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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What does cardinality refer to?
💡 Hint: Think about how we count elements in a bag.
Question 2
Easy
If set A has 3 elements, how many elements are in its power set?
💡 Hint: Remember the formula for the power 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 the cardinality relationship established by Cantor's theorem?
- The cardinality of set A is greater than the power set P(A)
- The cardinality of set A is less than the power set P(A)
- The cardinality of set A is equal to the power set P(A)
💡 Hint: Remember the definition of the power set.
Question 2
True or False: The power set of a finite set always contains 2^n elements, where n is the number of elements in that set.
- True
- False
💡 Hint: Think about the counting of subsets.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Construct an example of a finite set and calculate its power set, then identify its cardinality.
💡 Hint: List all possible subsets to ensure you haven't missed any.
Question 2
Explain the significance of Cantor's proof on the concept of different sizes of infinity. Provide a real-world analogy.
💡 Hint: Consider how different types of numbers can fill up the number line.
Challenge and get performance evaluation