Advanced Three-Set Inclusion–Exclusion and Set Analysis Quiz

1) For three sets A,B,C, which is the correct inclusion–exclusion formula for the union?

∣A∣+∣B∣+∣C∣−∣A∩B∩C∣

∣A∣+∣B∣+∣C∣−∣A∩B∣−∣A∩C∣

∣A∣+∣B∣+∣C∣−∣A∩B∣−∣A∩C∣−∣B∩C∣+∣A∩B∩C∣

∣A∩B∩C∣

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

Explanation

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

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) In universe 80 elements none count?

Union 60 → none 20.

Explanation

Union 60 → none 20.

3) Term sign triple intersection?

True

False

Triple always +.

Explanation

Triple always +.

4) None formula?

∣A∪B∪C∣

∣A^c∪B^c∪C^c∣

∣U∣−∣A∪B∪C∣

∣A^c∩B^c∩C^c∣+∣A∩B∩C∣

Outside union.

Explanation

Outside union.

5) Requires disjoint?

True

False

Handles overlap.

Explanation

Handles overlap.

6) Exactly two sets?

Sum pairs

Sum pairs−3 triple

Sum singles−union

Triple

Subtract triple appropriately.

Explanation

Subtract triple appropriately.

7) Solve triple given union etc?

True

False

Unique solution.

Explanation

Unique solution.

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∣?

21+19+17 − (8+6+5) + 4 = 42.

Explanation

21+19+17 − (8+6+5) + 4 = 42.

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

x = 7 from equation.

Explanation

x = 7 from equation.

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

Result 88.

Explanation

Result 88.

11) Probability at least one?

P(A)+P(B)+P(C)

P(A∪B∪C)

P(A)+P(B)+P(C)−...+P(A∩B∩C)

Both b) and c)

Both represent same.

Explanation

Both represent same.

12) To compute union needs?

Singles

Pairs

Triple

Complements

All required.

Explanation

All required.

Submit

13) Match formula parts

∣A∣+∣B∣+∣C∣

−(∣A∩B∣+∣A∩C∣+∣B∩C∣)

+∣A∩B∩C∣

Initial sum, subtract pairs, add triple.

Explanation

Initial sum, subtract pairs, add triple.

Submit

14) Group students at least one?

82.

Explanation

82.

15) None count?

90-82=8.

Explanation

90-82=8.

Advanced Three-Set Inclusion–Exclusion and Set Analysis Quiz

1) For three sets A,B,C, which is the correct inclusion–exclusion formula for the union?

2)

What first name or nickname would you like us to use?

2) In universe 80 elements none count?

3) Term sign triple intersection?

4) None formula?

5) Requires disjoint?

6) Exactly two sets?

7) Solve triple given union etc?

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∣?

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

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

11) Probability at least one?

12) To compute union needs?

13) Match formula parts

14) Group students at least one?

15) None count?