2.4.3. Part (b): Counting Bijective Functions

Try these first

1. 1.

   Define a bijection in your own words.

   Hint

   Think about injective and surjective functions.

2. 2.

   Is the function f: {1, 2, 3} → {4, 4, 4} a surjection?

   Hint

   Check if every element in the codomain has a pre-image.

3. 3.

   What is a bijective function?

   Hint

   Consider the definitions of injective and surjective functions.

4. 4.

   True or False: All surjective functions are bijective functions.

   • True
   • False

   Hint

   Think about the relationship between injectivity and surjectivity.

5. 5.

   Given two infinite sets A and B, describe a surjective function that is not bijective.

   Hint

   Use different relationships for mappings that overlap.

6. 6.

   How would you prove that every bijective function has an inverse? Discuss the relationship.

   Hint

   Focus on the uniqueness of mappings and how they allow reversibility.