Practice Cantor's Theorem (7) - Cantor's Theorem - Discrete Mathematics - Vol 2
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Cantor's Theorem

Practice - Cantor's Theorem

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Learning

Practice Questions

Test your understanding with targeted questions

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.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

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.

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

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.

Challenge 2 Hard

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.

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Reference links

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