21.1.15. Summary of Cardinality

Try these first

1. 1.

   Define cardinality in your own words.

   Hint

   Think about how you would count items in a box.

2. 2.

   What is a Catalan number?

   Hint

   Consider its use in counting valid parentheses.

3. 3.

   What is the cardinality of set A?

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

   Hint

   Remember how we select positions for parentheses.

4. 4.

   True or False: The reflection method helps in counting bad sequences.

   • True
   • False

   Hint

   Think about how reflection modifies sequences.

5. 5.

   Find the nth Catalan number for n=4 using any proven combinatorial method.

   Hint

   Follow the formula using the binomial coefficient.

6. 6.

   Given a specific sequence of 1s and -1s, identify whether it is valid or determine its fault using the reflection technique.

   Hint

   Use a sample case to illustrate.