Advanced Inclusion–Exclusion and Overlap-Correction Theory Quiz

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| Questions: 15 | Updated: Dec 1, 2025
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1) The inclusion–exclusion principle is primarily used to:

Explanation

It adjusts for elements counted more than once in overlaps.

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About This Quiz
Advanced Inclusionexclusion And Overlap-correction Theory Quiz - Quiz

Ready to explore inclusion–exclusion at an advanced, theory-driven level? This quiz moves into the deeper mechanics of intersection structures, sign patterns, and the logic behind counting complements or elements with multiple properties. You’ll apply rearranged formulas, consider complements, analyze divisibility problems, and work with multi-way intersections at a research-oriented precision.... see moreFrom probability identities to language enrollment problems, each question challenges you to interpret how overlap correction really works. By practicing these advanced tasks, you’ll see how inclusion–exclusion becomes a versatile framework for tackling complex combinatorial systems. see less

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2) For two finite sets A and B, which rearranged identity follows from inclusion–exclusion?

Explanation

Direct rearrangement from |A∪B| formula.

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3) If |A|=25, |B|=30, and |A∩B|=8, then |A∪B| equals:

Explanation

25 + 30 − 8 = 47.

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4) If |A∪B|=40, |A|=23, and |B|=28, then |A∩B| equals:

Explanation

23 + 28 − 40 = 11.

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5) In inclusion–exclusion, intersections of an odd number of sets appear with a plus sign.

Explanation

Sign is (−1)^(k+1).

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6) For three sets A, B, C, the term |A∩B∩C| appears with:

Explanation

Triple intersections are added.

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7) How many integers from 1 to 50 are divisible by 3 or 5?

Explanation

16 + 10 − 3 = 23.

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8) How many integers from 1 to 60 are divisible by 2 or 3?

Explanation

30 + 20 − 10 = 40.

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9) For events A and B, inclusion–exclusion gives:

Explanation

Same structure as sets.

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10) To find the probability that none occur, subtract the union from 1.

Explanation

P(none)=1−P(union).

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11) Inclusion–exclusion for three events A, B, C gives:

Explanation

Exact 3-event formula.

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12) Match the step with its role in inclusion–exclusion for three sets.

Explanation

Singles add, pairs subtract, triple adds.

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13) A standard way to define sets for inclusion–exclusion is to:

Explanation

Each set corresponds to one property.

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14) Inclusion–exclusion can count elements satisfying at least r properties.

Explanation

Requires grouping intersections appropriately.

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15) 90 students: 36 French, 32 German, 30 Spanish; intersections 14, 12, 10; triple 8. How many study ≥1?

Explanation

36+32+30 − (14+12+10) + 8 = 70.

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The inclusion–exclusion principle is primarily used to:
For two finite sets A and B, which rearranged identity follows from...
If |A|=25, |B|=30, and |A∩B|=8, then |A∪B| equals:
If |A∪B|=40, |A|=23, and |B|=28, then |A∩B| equals:
In inclusion–exclusion, intersections of an odd number of sets...
For three sets A, B, C, the term |A∩B∩C| appears with:
How many integers from 1 to 50 are divisible by 3 or 5?
How many integers from 1 to 60 are divisible by 2 or 3?
For events A and B, inclusion–exclusion gives:
To find the probability that none occur, subtract the union from 1.
Inclusion–exclusion for three events A, B, C gives:
Match the step with its role in inclusion–exclusion for three sets.
A standard way to define sets for inclusion–exclusion is to:
Inclusion–exclusion can count elements satisfying at least r...
90 students: 36 French, 32 German, 30 Spanish; intersections 14, 12,...
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