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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 = {a, b}?
💡 Hint: Remember, the power set includes all subsets.
Question 2
Easy
Define cardinality.
💡 Hint: Think about how to measure the size of a 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 relationship between a set and its power set according to Cantor's Theorem?
- The sizes are equal
- The power set is larger
- The power set is smaller
💡 Hint: Think about how many subsets can be formed.
Question 2
True or False: A power set of a finite set always has a finite number of elements.
- True
- False
💡 Hint: Consider the formula for power sets.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Construct a set A with 4 elements and illustrate the power set P(A). Explain the relationship of sizes.
💡 Hint: Count the number of subsets and relate it back to the power set definition.
Question 2
Explain how Cantor's diagonalization argument not only proves the non-existence of a surjective function but also illustrates the concept of uncountability.
💡 Hint: Reflect on the steps in constructing the diagonal set.
Challenge and get performance evaluation