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

Practice: Extension to Three Sets

Lesson 22.1.2Counting Using Principle of Inclusion-Exclusion

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8 questions

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6 sample questions

Question 1.
What is the cardinality of the union of sets A = {1, 2} and B = {2, 3}?
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Remember to subtract the intersection.
Question 2.
If A = {1, 2, 3} and B = {2, 3, 4}, what is |A ∩ B|?
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List the common elements.
3Question 3.
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
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Think about what union means.
4Question 4.
True or False: The intersection must always be subtracted in the inclusion-exclusion principle.
- True
- False
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Reflect on the role of overlaps.
Question 5.
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|.
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Follow the inclusion-exclusion formula step by step.
Question 6.
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|.
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Tally each term carefully as directed.

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