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Practice Questions
Test your understanding with targeted questions related to the topic.
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.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
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.
Solve 2 more questions and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Determine and prove the relationship between Catalan numbers and balanced parenthesis sequences.
💡 Hint: Consider how bounding conditions on sequences relate to parentheses.
Question 2
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.
Challenge and get performance evaluation