Practice Finding Onto Functions (22.2.2) - Counting Using Principle of Inclusion-Exclusion

Practice: Finding Onto Functions

Lesson 22.2.2Counting Using Principle of Inclusion-Exclusion

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8 questions

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6 sample questions

Question 1.
What is the cardinality of a set with 5 elements?
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Count the number of elements.
Question 2.
State the formula for two sets using the inclusion-exclusion principle.
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Think about overlapping elements.
3Question 3.
What does the inclusion-exclusion principle help us calculate?
- Cardinality of individual sets
- Cardinality of the union of sets
- Cardinality of intersections
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Think about what cardinality means!
4Question 4.
True or False: An onto function can have unused elements in its codomain.
- True
- False
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Reflect on the idea of mapping elements.
Question 5.
How many onto functions exist from a set with 8 elements into a set with 4 elements? Use the inclusion-exclusion principle.
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Start by calculating the function counts and then break down the exclusion cases.
Question 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.
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Consider the total assignments and the necessary exclusions for empty assignments.

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