Practice Introduction To The Principle Of Inclusion-exclusion (22.1.1) - Counting Using Principle of Inclusion-Exclusion

Practice: Introduction to the Principle of Inclusion-Exclusion

Lesson 22.1.1Counting 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 the union of two sets A and B, given |A|=10 and |B|=12 with |A ∩ B|=5?
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Use the union formula.
Question 2.
Define what is meant by 'intersection' in set theory.
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Think about shared elements.
3Question 3.
What formula would you use to find the number of elements in |A ∪ B|?
- |A| + |B|
- |A| + |B| - |A ∩ B|
- |A| - |B|
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Remember why we subtract the intersection!
4Question 4.
True or False: The principle of inclusion-exclusion can be applied to more than two sets.
- True
- False
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Think about how we can add more elements.
Question 5.
You have three sets: A has 5 elements, B has 3 elements, and C has 4. The intersections are |A ∩ B| = 2, |A ∩ C| = 1, |B ∩ C| = 1 and |A ∩ B ∩ C| = 0. Calculate |A ∪ B ∪ C|.
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Follow the inclusion-exclusion steps carefully.
Question 6.
Draw a Venn diagram for two sets A and B with |A|=6, |B|=4, and |A ∩ B|=2. Label the individual regions.
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Consider each section of the diagram and how they relate.

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