21.1.5. Cardinality of Set A

Try these first

1. 1.

   What is the cardinality of set A for n=2?

   Hint

   Use the binomial coefficient formula.

2. 2.

   Define one key property of valid sequences.

   Hint

   Think about how we sum the elements as we go.

3. 3.

   What is the formula for the size of set A?

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

   Hint

   Recall binomial coefficient properties.

4. 4.

   True or False: Set B contains all valid sequences.

   • True
   • False

   Hint

   Think about what defines valid and invalid sequences.

5. 5.

   If n=5, determine the total valid sequences using both set cardinalities and the Catalan number formula.

   Hint

   Work the formulas through step by step to count each set.

6. 6.

   Illustrate where Catalan numbers appear in real-world structures. Construct a problem involving paths or trees that could use these principles.

   Hint

   Relate back to the definitions and their applications.