Practice Cardinality Of Set B (21.1.6) - Catalan Numbers - Derivation of Closed Form Formula
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Cardinality of Set B

Practice - Cardinality of Set B

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Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What is the cardinality of Set A for n=3?

💡 Hint: Use the formula C(2n, n).

Question 2 Easy

How do you define a bad sequence?

💡 Hint: Consider the properties of 1s and -1s.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the correct formula for the number of sequences in set A?

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

💡 Hint: Look for the definition of set A.

Question 2

Does a bad sequence have no negative partial sums?

True
False

💡 Hint: Recall the definition of bad sequences.

2 more questions available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Determine and prove the relationship between Catalan numbers and balanced parenthesis sequences.

💡 Hint: Consider how bounding conditions on sequences relate to parentheses.

Challenge 2 Hard

Using the reflection method, demonstrate the equality of set B and set C through an example with n=3.

💡 Hint: Work through each bad sequence step-by-step in transforming it.

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