2.2. Question 6: Surjective Function

Try these first

1. 1.

   Define a surjective function.

   Hint

   Think of how each output is achieved through inputs.

2. 2.

   List one property of bijective functions.

   Hint

   Recall the letter B represents both properties.

3. 3.

   What is a surjective function?

   Hint

   Consider the mapping of inputs to outputs.

4. 4.

   If a function is surjective and operates over a finite set, is it also bijective?

   • True
   • False

   Hint

   Think about what happens when the number of elements match.

5. 5.

   Prove that every surjective function from a finite set to itself is bijective.

   Hint

   Consider the cardinality of the domain and codomain.

6. 6.

   Construct a surjective function from {1, 2, 3, 4} to {A, B} that is not injective, and explain why.

   Hint

   Analyze how many distinct inputs share the same output.