21.1.6. Cardinality of Set B

Try these first

1. 1.

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

   Hint

   Use the formula C(2n, n).

2. 2.

   How do you define a bad sequence?

   Hint

   Consider the properties of 1s and -1s.

3. 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)

   Hint

   Look for the definition of set A.

4. 4.

   Does a bad sequence have no negative partial sums?

   • True
   • False

   Hint

   Recall the definition of bad sequences.

5. 5.

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

   Hint

   Consider how bounding conditions on sequences relate to parentheses.

6. 6.

   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.