Practice Cardinality Of Set B (21.1.6) - Catalan Numbers

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6 sample questions

Question 1.
What is the cardinality of Set A for n=3?
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Use the formula C(2n, n).
Question 2.
How do you define a bad sequence?
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Consider the properties of 1s and -1s.
3Question 3.
What is the correct formula for the number of sequences in set A?
- C(2n
- n)
- C(2n
- n+1)
- C(2n-1
- n)
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Look for the definition of set A.
4Question 4.
Does a bad sequence have no negative partial sums?
- True
- False
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Recall the definition of bad sequences.
Question 5.
Determine and prove the relationship between Catalan numbers and balanced parenthesis sequences.
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Consider how bounding conditions on sequences relate to parentheses.
Question 6.
Using the reflection method, demonstrate the equality of set B and set C through an example with n=3.
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Work through each bad sequence step-by-step in transforming it.

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