2. Discrete Mathematics

Try these first

1. 1.

   Define a surjective function.

   Hint

   Think of it as every 'output' must have at least one 'input'.

2. 2.

   What is an injective function?

   Hint

   Does every unique input need to yield a unique output?

3. 3.

   What defines a surjective function?

   • Each element in the codomain has at least one corresponding pre-image.
   • No two inputs map to the same output.
   • Both A and B.

   Hint

   Focus on what needs to be covered in terms of outputs.

4. 4.

   True or False: Every bijective function is also surjective.

   • True
   • False

   Hint

   Consider the definitions of the terms involved.

5. 5.

   Construct a surjective function from the set {1, 2, 3, 4} to {A, B} and describe its properties.

   Hint

   Keep in mind the requirements for surjectiveness.

6. 6.

   Provide a proof using induction that the number of bijective functions from a set of size n to itself is n!.

   Hint

   Use the principle of mathematical induction to structure your proof.