Advanced Three-Set Inclusion–Exclusion and Set Analysis Quiz

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| Questions: 15 | Updated: Dec 16, 2025
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Question 1 / 16
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1) For three sets A,B,C, which is the correct inclusion–exclusion formula for the union?

Explanation

Three-set inclusion–exclusion = singles − all pairs + triple.

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About This Quiz
Advanced Three-set Inclusionexclusion And Set Analysis Quiz - Quiz

Ready to push your understanding of three-set inclusion–exclusion to a more advanced level? In this quiz, you’ll work with precise formulas, rearrangements, and logical consequences of set relationships. You’ll use union sizes, pairwise intersections, and total population counts to deduce triple intersections and “none” counts, and you’ll connect counting versions... see moreof inclusion–exclusion with their probability counterparts. You’ll also interpret what conditions like ∣A ∪ B ∪ C∣ = ∣A∣ + ∣B∣ + ∣C∣ or known intersection patterns really tell you about how the sets overlap. By the end, you’ll have a deeper, more rigorous view of how inclusion–exclusion organizes complex overlaps into a clean and powerful counting principle.
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2)
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2) In universe 80 elements none count?

Explanation

Union 60 → none 20.

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3) Term sign triple intersection?

Explanation

Triple always +.

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4) None formula?

Explanation

Outside union.

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5) Requires disjoint?

Explanation

Handles overlap.

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6) Exactly two sets?

Explanation

Subtract triple appropriately.

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7) Solve triple given union etc?

Explanation

Unique solution.

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8) Let ∣A∣=21, ∣B∣=19, ∣C∣=17; ∣A∩B∣=8, ∣A∩C∣=6, ∣B∩C∣=5; and ∣A∩B∩C∣=4. What is ∣A∪B∪C∣?

Explanation

21+19+17 − (8+6+5) + 4 = 42.

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9) For sets A,B,C with given values find ∣A∩B∩C∣.

Explanation

x = 7 from equation.

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10) Divisible by 2,3,5 from 1..120?

Explanation

Result 88.

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11) Probability at least one?

Explanation

Both represent same.

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12) To compute union needs?

Explanation

All required.

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13) Match formula parts

Explanation

Initial sum, subtract pairs, add triple.

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14) Group students at least one?

Explanation

82.

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15) None count?

Explanation

90-82=8.

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For three sets A,B,C, which is the correct inclusion–exclusion...
In universe 80 elements none count?
Term sign triple intersection?
None formula?
Requires disjoint?
Exactly two sets?
Solve triple given union etc?
Let ∣A∣=21, ∣B∣=19, ∣C∣=17; ∣A∩B∣=8, ∣A∩C∣=6,...
For sets A,B,C with given values find ∣A∩B∩C∣.
Divisible by 2,3,5 from 1..120?
Probability at least one?
To compute union needs?
Match formula parts
Group students at least one?
None count?
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