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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 the set {a, b}?
💡 Hint: List all possible subsets.
Question 2
Easy
Is the cardinality of {1, 2} greater than, less than, or equal to its power set?
💡 Hint: Consider how many subsets there are.
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 the cardinality of a set and its power set?
- They are equal
- Power set is greater
- Power set is lesser
💡 Hint: Reflect on the relationship between a set and all of its subsets.
Question 2
Is the following statement true or false? 'The power set of a finite set is also finite.'
- True
- False
💡 Hint: Consider the formula for the size of the power set.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Prove using Cantor's theorem that the set of real numbers cannot be put into one-to-one correspondence with the natural numbers.
💡 Hint: Think about how you would apply the diagonal method to generate a new number.
Question 2
Consider a set B. If the cardinality of B is 5, determine the cardinality of P(B) and describe what this means in terms of Cantor's theorem.
💡 Hint: Use the exponential relationship between set size and power sets.
Challenge and get performance evaluation