Inclusion–Exclusion with Two Sets Quiz

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| Questions: 15 | Updated: Dec 1, 2025
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1) For two sets A and B, the inclusion–exclusion formula is:

Explanation

Subtract |A∩B| to correct for double counting.

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About This Quiz
Inclusionexclusion With Two Sets Quiz - Quiz

Are you ready to see how overlapping sets can be counted accurately? In this quiz, you’ll explore the classic inclusion–exclusion formula for two sets and learn how it fixes the problem of double-counting shared elements. You’ll work through clear numerical examples, survey-style word problems, and simple applications using complements and... see more“exactly one” scenarios. From coffee-and-tea preferences to numbers divisible by 4 or 6, you’ll get comfortable computing unions, intersections, and elements in neither set. By the end, you’ll be able to handle two-set Venn diagram questions with confidence and understand exactly why the formula ∣A ∪ B∣ = ∣A∣ + ∣B∣ − ∣A ∩ B∣ is so powerful. see less

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2) If |A|=18, |B|=12, and |A∩B|=5, then |A∪B| equals:

Explanation

18 + 12 – 5 = 25.

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3) If |A∪B|=40, |A|=25, and |B|=22, then |A∩B| equals:

Explanation

25 + 22 – 40 = 7.

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4) If A and B are disjoint, then |A∪B| = |A| + |B|.

Explanation

Disjoint sets have |A∩B|=0.

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5) For any sets A and B, |A∩B| ≤ |A| and |A∩B| ≤ |B|.

Explanation

The intersection cannot exceed either set.

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6) In a survey, 30 students like coffee, 20 like tea, and 10 like both. How many like coffee or tea (or both)?

Explanation

30 + 20 − 10 = 40.

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7) If |A|=15, |B|=15, and |A∪B|=20, then |A∩B| equals:

Explanation

15 + 15 – 20 = 10.

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8) Among the numbers 1 to 60, how many are divisible by 4 or 6?

Explanation

15 + 10 − 5 = 20.

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9) If |A∪B| = |A| + |B|, then A and B must be disjoint.

Explanation

Equality means |A∩B| = 0.

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10) Which expression counts the elements that are in exactly one of A or B?

Explanation

Subtract intersection twice to exclude shared elements.

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11) A universal set U has 50 elements. If |A| = 30 and |Aᶜ| = x, then x equals:

Explanation

Complement size = 50 - 30 = 20.

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12) For two sets A and B, |A ∪ Bᶜ| = |U| − |B∖A|.

Explanation

A ∪ Bᶜ is complement of B∖A.

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13) 100 people: 60 like apples, 50 like bananas. Minimum liking both?

Explanation

Minimum overlap = 60 + 50 − 100 = 10.

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14) Same group: maximum liking both apples & bananas?

Explanation

Max overlap is min(60, 50) = 50.

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15) If |A|=15, |B|=10, and |A∩B|=0, then |A∪B|=25.

Explanation

Disjoint sets add directly.

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For two sets A and B, the inclusion–exclusion formula is:
If |A|=18, |B|=12, and |A∩B|=5, then |A∪B| equals:
If |A∪B|=40, |A|=25, and |B|=22, then |A∩B| equals:
If A and B are disjoint, then |A∪B| = |A| + |B|.
For any sets A and B, |A∩B| ≤ |A| and |A∩B| ≤ |B|.
In a survey, 30 students like coffee, 20 like tea, and 10 like both....
If |A|=15, |B|=15, and |A∪B|=20, then |A∩B| equals:
Among the numbers 1 to 60, how many are divisible by 4 or 6?
If |A∪B| = |A| + |B|, then A and B must be disjoint.
Which expression counts the elements that are in exactly one of A or...
A universal set U has 50 elements. If |A| = 30 and |Aᶜ| = x, then x...
For two sets A and B, |A ∪ Bᶜ| = |U| − |B∖A|.
100 people: 60 like apples, 50 like bananas. Minimum liking both?
Same group: maximum liking both apples & bananas?
If |A|=15, |B|=10, and |A∩B|=0, then |A∪B|=25.
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