Practice Generalization To N Sets (22.1.3) - Counting Using Principle of Inclusion-Exclusion

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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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Consider what elements are shared.
Question 2.
How does adding the intersection help when calculating union?
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Think about how many times each element appears.
3Question 3.
What does the principle of inclusion-exclusion help prevent?
- A) Over-counting elements
- B) Under-counting elements
- C) Both A and B
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Think about how the overlap is handled.
4Question 4.
In how many ways can the intersection of n sets be expressed?
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Remember the pattern with positive and negative signs.
Question 5.
Given sets A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, and C = {5, 6, 7, 8}, calculate |A ∪ B ∪ C|.
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Use inclusion-exclusion carefully for intersections.
Question 6.
If A1 to A5 have 3, 4, 5, 6, and 7 elements respectively, what is |A1 ∪ A2 ∪ A3 ∪ A4 ∪ A5| if some intersections are known?
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Each intersection adjusts the counting!

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