2.6.4. Part (d): Surjectivity of f

Try these first

1. 1.

   Define a surjective function.

   Hint

   Think about covering all elements in the codomain.

2. 2.

   Can a surjective function be injective? Provide an example.

   Hint

   Recall the definition of both terms.

3. 3.

   What is a surjective function?

   • A function that is one-to-one.
   • A function where every element of codomain has a pre-image.
   • A function that is injective.

   Hint

   Think about every element in the target set.

4. 4.

   In finite sets, a surjective function is also:

   • True
   • False

   Hint

   Consider the implications of finite mappings.

5. 5.

   Given a set A = {1, 2, 3, 4}, find surjective functions to set B = {x1, x2, x3}. What are the conditions?

   Hint

   Use combinations to ensure all elements in B are met.

6. 6.

   Construct a proof showing why a surjective function from a finite set with n elements is also bijective.

   Hint

   Consider elements assigned during surjectivity.