2.1.1. Introduction

Try these first

1. 1.

   Define a surjective function in your own words.

   Hint

   Think about the elements in both sets and how they relate.

2. 2.

   What is S(n, k) in terms of Stirling numbers?

   Hint

   Consider the connection to set partitions.

3. 3.

   What is a surjective function?

   • A function where every element in the domain is unique.
   • A function where every codomain element has at least one pre-image.
   • A function that is always linear.

   Hint

   Think about the relationship between the domain and codomain elements.

4. 4.

   Is a bijective function always injective?

   • True
   • False

   Hint

   Recall the definitions of injective and bijective functions.

5. 5.

   Given a set of size 5, how many different surjective functions can be created to a set of size 3?

   Hint

   Remember to break it down into partitions and mappings.

6. 6.

   Prove that there exists a surjective function that is not injective by constructing a specific example.

   Hint

   Focus on the mappings from domain to codomain.