Practice Proof Of The General Formula (22.1.4) - Counting Using Principle of Inclusion-Exclusion
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Proof of the General Formula

Practice - Proof of the General Formula

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Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What is the cardinality of the union of sets A={1,2,3} and B={2,3,4}?

💡 Hint: Count the total unique elements.

Question 2 Easy

Define the term 'cardinality'.

💡 Hint: Think about how many different items you have.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the principle of inclusion-exclusion primarily used for?

Establishing set relationships
Counting elements in overlapping sets
Finding set intersections

💡 Hint: Think about what complication overlaps create when counting.

Question 2

True or False: The cardinality of |A ∪ B| is equal to |A| + |B| only if there is no overlap.

True
False

💡 Hint: Consider how overlaps affect counts.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Given sets A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8}. Calculate |A ∪ B ∪ C|.

💡 Hint: Follow the general formula for three sets carefully.

Challenge 2 Hard

Using the principle of inclusion-exclusion, prove for n = 4 sets that |A1 ∪ A2 ∪ A3 ∪ A4| can be expanded in terms of their pairwise and higher-order intersections.

💡 Hint: Ensure every intersection's contribution is correctly signed and counted.

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