Practice Extension To Three Sets (22.1.2) - Counting Using Principle of Inclusion-Exclusion
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Extension to Three Sets

Practice - Extension to Three Sets

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Practice Questions

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Question 1 Easy

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

💡 Hint: Remember to subtract the intersection.

Question 2 Easy

If A = {1, 2, 3} and B = {2, 3, 4}, what is |A ∩ B|?

💡 Hint: List the common elements.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What does the inclusion-exclusion principle help calculate?

The size of a single set
The size of the union of multiple sets
The size of intersection only

💡 Hint: Think about what union means.

Question 2

True or False: The intersection must always be subtracted in the inclusion-exclusion principle.

True
False

💡 Hint: Reflect on the role of overlaps.

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Given sets A, B, C with cardinalities |A|=5, |B|=7, |C|=3, |A ∩ B|=2, |A ∩ C|=1, |B ∩ C|=1, |A ∩ B ∩ C|=0, find |A ∪ B ∪ C|.

💡 Hint: Follow the inclusion-exclusion formula step by step.

Challenge 2 Hard

Consider four sets P, Q, R, S where |P|=6, |Q|=5, |R|=4, |S|=3 and every intersection where two sets meet is 1, and three sets meet is 0. Calculate |P ∪ Q ∪ R ∪ S|.

💡 Hint: Tally each term carefully as directed.

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