Practice Cardinality Of Set A (21.1.5) - Catalan Numbers - Derivation of Closed Form Formula
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Cardinality of Set A

Practice - Cardinality of Set A

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Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What is the cardinality of set A for n=2?

💡 Hint: Use the binomial coefficient formula.

Question 2 Easy

Define one key property of valid sequences.

💡 Hint: Think about how we sum the elements as we go.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the formula for the size of set A?

C(2n
n)
C(2n
n + 1)
C(n
n)

💡 Hint: Recall binomial coefficient properties.

Question 2

True or False: Set B contains all valid sequences.

True
False

💡 Hint: Think about what defines valid and invalid sequences.

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

If n=5, determine the total valid sequences using both set cardinalities and the Catalan number formula.

💡 Hint: Work the formulas through step by step to count each set.

Challenge 2 Hard

Illustrate where Catalan numbers appear in real-world structures. Construct a problem involving paths or trees that could use these principles.

💡 Hint: Relate back to the definitions and their applications.

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