Practice Generalization For M And N Elements (22.2.3) - Counting Using Principle of Inclusion-Exclusion

Practice: Generalization for m and n Elements

Lesson 22.2.3Counting Using Principle of Inclusion-Exclusion

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8 questions

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6 sample questions

Question 1.
Calculate |A ∪ B| if |A|=5, |B|=3, and |A ∩ B|=1.
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Use the formula for two sets.
Question 2.
What is the cardinality of the union of two disjoint sets |A|=4 and |B|=5?
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If sets are disjoint, there’s no intersection to subtract.
3Question 3.
What is the general formula for the union of two sets?
- |A| + |B|
- |A| + |B| - |A ∩ B|
- |A| - |B|
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Review the principle of inclusion-exclusion.
4Question 4.
True or False: Inclusion-Exclusion can only be applied to two sets.
- True
- False
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Think about how we extended the concept from two to three sets.
Question 5.
Four students register for three different classes, with some taking multiple classes. How many unique student registrations can be calculated using the principle?
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List out overlaps carefully.
Question 6.
You have 5 distinct colors; how can you calculate the distinct patterns you can create using the inclusion-exclusion principle if some colors must overlap?
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Map your color set accurately to find overlaps.

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