22.2.2. Finding Onto Functions

Try these first

1. 1.

   What is the cardinality of a set with 5 elements?

   Hint

   Count the number of elements.

2. 2.

   State the formula for two sets using the inclusion-exclusion principle.

   Hint

   Think about overlapping elements.

3. 3.

   What does the inclusion-exclusion principle help us calculate?

   • Cardinality of individual sets
   • Cardinality of the union of sets
   • Cardinality of intersections

   Hint

   Think about what cardinality means!

4. 4.

   True or False: An onto function can have unused elements in its codomain.

   • True
   • False

   Hint

   Reflect on the idea of mapping elements.

5. 5.

   How many onto functions exist from a set with 8 elements into a set with 4 elements? Use the inclusion-exclusion principle.

   Hint

   Start by calculating the function counts and then break down the exclusion cases.

6. 6.

   Design a problem set that requires students to find the number of ways to assign 10 different tasks to 5 workers so that each worker has at least one task.

   Hint

   Consider the total assignments and the necessary exclusions for empty assignments.