Practice Schroder-bernstein Theorem (4.3.2) - Module No # 05 - Discrete Mathematics - Vol 2
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Schroder-Bernstein Theorem

Practice - Schroder-Bernstein Theorem

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Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What is an injective function?

💡 Hint: Think of a one-to-one relationship.

Question 2 Easy

Does the function f(x) = x^2 is injective for positive integers?

💡 Hint: Check if any two inputs lead to the same output.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What does the Schroder-Bernstein theorem establish about the cardinalities of sets?

They can never be equal
They are equal if both have injective functions
They are always infinite

💡 Hint: Think back to the conditions required for the theorem.

Question 2

True or False: If |A| ≤ |B|, it necessarily means A is larger than B.

True
False

💡 Hint: Refer to the definition of cardinality.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Prove that the set of all rational numbers is countably infinite using the concepts from the Schroder-Bernstein theorem.

💡 Hint: Use the structured nature of rational numbers to establish your mappings.

Challenge 2 Hard

Show two sets, one infinite and one finite, and explain how this relates to the application of the Schroder-Bernstein theorem.

💡 Hint: Consider graphing both sets to visualize the relationships.

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