Practice - Construction of the Subset S
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Practice Questions
Test your understanding with targeted questions
What is the power set of the set {a, b}?
💡 Hint: List all possible subsets.
Is the cardinality of {1, 2} greater than, less than, or equal to its power set?
💡 Hint: Consider how many subsets there are.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What does Cantor's theorem state about the cardinality of a set and its power set?
💡 Hint: Reflect on the relationship between a set and all of its subsets.
Is the following statement true or false? 'The power set of a finite set is also finite.'
💡 Hint: Consider the formula for the size of the power set.
1 more question available
Challenge Problems
Push your limits with advanced challenges
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.
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.
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