3.1. Cardinality of Finite Sets

Try these first

1. 1.

   What is the cardinality of the set {Cat, Dog, Fish}?

   Hint

   Count the number of elements.

2. 2.

   True or false: |{Apple, Banana}| = |{1, 2, 3}?

   Hint

   Compare the number of elements in each set.

3. 3.

   What does the notation |X| represent?

   • The dimensions of set X
   • The cardinality of set X
   • The elements in set X

   Hint

   Think of cardinality as counting.

4. 4.

   True or False: A bijection implies that the two sets have the same number of elements.

   • True
   • False

   Hint

   Remember the definition of bijection.

5. 5.

   Demonstrate why the set of all even integers is countable and establish a bijection to the positive integers.

   Hint

   Consider how each positive integer relates to an even integer.

6. 6.

   Find all the possible bijections between the sets A = {1, 2} and B = {x, y}.

   Hint

   Count how many ways to pair elements uniquely.