Practice - Counting Using Principle of Inclusion-Exclusion
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Practice Questions
Test your understanding with targeted questions
What is the formula for the cardinality of the union of two sets?
💡 Hint: Think about over-counting!
If |A| = 5 and |B| = 3, and |A ∩ B| = 2, what's |A ∪ B|?
💡 Hint: Use the formula for union!
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
How does the principle of inclusion-exclusion help in counting?
💡 Hint: Think about adding and subtracting counts.
The formula for three sets' union primarily adjusts for what?
💡 Hint: Remember the addition and subtraction scheme!
1 more question available
Challenge Problems
Push your limits with advanced challenges
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.
💡 Hint: Set up each count and adjust using the intersection.
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.
💡 Hint: Extract each size and substitute into the inclusion-exclusion formula.
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