Practice Counting Using Principle Of Inclusion-exclusion (22.1) - Counting Using Principle of Inclusion-Exclusion

Practice: Counting Using Principle of Inclusion-Exclusion

Lesson 22.1Counting Using Principle of Inclusion-Exclusion

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9 questions

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3 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
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Quiz
3 questions · about 2 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
What is the formula for the cardinality of the union of two sets?
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Think about over-counting!
Question 2.
If |A| = 5 and |B| = 3, and |A ∩ B| = 2, what's |A ∪ B|?
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Use the formula for union!
3Question 3.
How does the principle of inclusion-exclusion help in counting?
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Think about adding and subtracting counts.
4Question 4.
The formula for three sets' union primarily adjusts for what?
- True
- False
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Remember the addition and subtraction scheme!
Question 5.
In a conference, 100 attendees discussed several topics. If 70 were interested in AI, 50 in Data Science, and 30 in both, determine how many were interested in at least one topic.
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Set up each count and adjust using the intersection.
Question 6.
Consider three libraries A, B, and C with 100, 80, and 60 titles respectively, with overlaps: 30 common in A and B, 20 in A and C, 25 between B and C, and 15 in all three. Find the number of unique titles.
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Extract each size and substitute into the inclusion-exclusion formula.

5 more questions in this section. Enroll free to practise them all.