Practice Introduction To Cardinality (7.1) - Cantor's Theorem - Discrete Mathematics - Vol 2
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Introduction to Cardinality

Practice - Introduction to Cardinality

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Practice Questions

Test your understanding with targeted questions

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.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

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.

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

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.

Challenge 2 Hard

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.

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