ReasoningAges 16-18

Universal set & Venn complements

Use inclusion-exclusion within a universal set to find how many items belong to neither subset. Review suitability for your learners before teaching.

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Age band:Ages 13-15 Ages 16-18

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Worksheet StudioPractice pack · Ages 16-18

Universal set & Venn complements

Take your time. Show your thinking.

1. In a group of 37 students, n(A) = 14, n(B) = 25, and n(A ∩ B) = 10. How many students are in neither A nor B?
37 s · 14 · 25 · 10 · Universal set & Venn compl…
2. In a group of 48 students, n(A) = 32, n(B) = 16, and n(A ∩ B) = 12. How many students are in neither A nor B?
48 s · 32 · 16 · 12 · Universal set & Venn compl…
3. In a group of 41 students, n(A) = 18, n(B) = 21, and n(A ∩ B) = 8. How many students are in neither A nor B?
41 s · 18 · 21 · 8 · Universal set & Venn compl…
4. In a group of 55 students, n(A) = 26, n(B) = 29, and n(A ∩ B) = 10. How many students are in neither A nor B?
55 s · 26 · 29 · 10 · Universal set & Venn compl…
5. In a group of 30 students, n(A) = 18, n(B) = 14, and n(A ∩ B) = 8. How many students are in neither A nor B?
30 s · 18 · 14 · 8 · Universal set & Venn compl…
6. In a group of 30 students, n(A) = 18, n(B) = 8, and n(A ∩ B) = 3. How many students are in neither A nor B?
30 s · 18 · 8 · 3 · Universal set & Venn compl…
7. In a group of 28 students, n(A) = 11, n(B) = 15, and n(A ∩ B) = 6. How many students are in neither A nor B?
28 s · 11 · 15 · 6 · Universal set & Venn compl…
8. In a group of 39 students, n(A) = 8, n(B) = 16, and n(A ∩ B) = 3. How many students are in neither A nor B?
39 s · 8 · 16 · 3 · Universal set & Venn compl…
9. In a group of 43 students, n(A) = 25, n(B) = 22, and n(A ∩ B) = 11. How many students are in neither A nor B?
43 s · 25 · 22 · 11 · Universal set & Venn compl…
10. In a group of 41 students, n(A) = 17, n(B) = 19, and n(A ∩ B) = 12. How many students are in neither A nor B?
41 s · 17 · 19 · 12 · Universal set & Venn compl…
11. In a group of 30 students, n(A) = 19, n(B) = 17, and n(A ∩ B) = 10. How many students are in neither A nor B?
30 s · 19 · 17 · 10 · Universal set & Venn compl…
12. In a group of 56 students, n(A) = 29, n(B) = 32, and n(A ∩ B) = 12. How many students are in neither A nor B?
56 s · 29 · 32 · 12 · Universal set & Venn compl…

12 questions · Seed 104734 · Age guidance, not curriculum certification

View the answer key

Worksheet StudioAnswer key · Ages 16-18

Universal set & Venn complements

Answers and reasoning. Review before teaching.

1. In a group of 37 students, n(A) = 14, n(B) = 25, and n(A ∩ B) = 10. How many students are in neither A nor B?
8
By inclusion-exclusion, n(A ∪ B) = 14 + 25 − 10 = 29, leaving 37 − 29 = 8 in neither set.
2. In a group of 48 students, n(A) = 32, n(B) = 16, and n(A ∩ B) = 12. How many students are in neither A nor B?
12
By inclusion-exclusion, n(A ∪ B) = 32 + 16 − 12 = 36, leaving 48 − 36 = 12 in neither set.
3. In a group of 41 students, n(A) = 18, n(B) = 21, and n(A ∩ B) = 8. How many students are in neither A nor B?
10
By inclusion-exclusion, n(A ∪ B) = 18 + 21 − 8 = 31, leaving 41 − 31 = 10 in neither set.
4. In a group of 55 students, n(A) = 26, n(B) = 29, and n(A ∩ B) = 10. How many students are in neither A nor B?
10
By inclusion-exclusion, n(A ∪ B) = 26 + 29 − 10 = 45, leaving 55 − 45 = 10 in neither set.
5. In a group of 30 students, n(A) = 18, n(B) = 14, and n(A ∩ B) = 8. How many students are in neither A nor B?
6
By inclusion-exclusion, n(A ∪ B) = 18 + 14 − 8 = 24, leaving 30 − 24 = 6 in neither set.
6. In a group of 30 students, n(A) = 18, n(B) = 8, and n(A ∩ B) = 3. How many students are in neither A nor B?
7
By inclusion-exclusion, n(A ∪ B) = 18 + 8 − 3 = 23, leaving 30 − 23 = 7 in neither set.
7. In a group of 28 students, n(A) = 11, n(B) = 15, and n(A ∩ B) = 6. How many students are in neither A nor B?
8
By inclusion-exclusion, n(A ∪ B) = 11 + 15 − 6 = 20, leaving 28 − 20 = 8 in neither set.
8. In a group of 39 students, n(A) = 8, n(B) = 16, and n(A ∩ B) = 3. How many students are in neither A nor B?
18
By inclusion-exclusion, n(A ∪ B) = 8 + 16 − 3 = 21, leaving 39 − 21 = 18 in neither set.
9. In a group of 43 students, n(A) = 25, n(B) = 22, and n(A ∩ B) = 11. How many students are in neither A nor B?
7
By inclusion-exclusion, n(A ∪ B) = 25 + 22 − 11 = 36, leaving 43 − 36 = 7 in neither set.
10. In a group of 41 students, n(A) = 17, n(B) = 19, and n(A ∩ B) = 12. How many students are in neither A nor B?
17
By inclusion-exclusion, n(A ∪ B) = 17 + 19 − 12 = 24, leaving 41 − 24 = 17 in neither set.
11. In a group of 30 students, n(A) = 19, n(B) = 17, and n(A ∩ B) = 10. How many students are in neither A nor B?
4
By inclusion-exclusion, n(A ∪ B) = 19 + 17 − 10 = 26, leaving 30 − 26 = 4 in neither set.
12. In a group of 56 students, n(A) = 29, n(B) = 32, and n(A ∩ B) = 12. How many students are in neither A nor B?
7
By inclusion-exclusion, n(A ∪ B) = 29 + 32 − 12 = 49, leaving 56 − 49 = 7 in neither set.

12 questions · Seed 104734 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 16-18

Universal set & Venn complements

Take your time. Show your thinking.

1. In a group of 37 students, n(A) = 14, n(B) = 25, and n(A ∩ B) = 10. How many students are in neither A nor B?
37 s · 14 · 25 · 10 · Universal set & Venn compl…
2. In a group of 48 students, n(A) = 32, n(B) = 16, and n(A ∩ B) = 12. How many students are in neither A nor B?
48 s · 32 · 16 · 12 · Universal set & Venn compl…
3. In a group of 41 students, n(A) = 18, n(B) = 21, and n(A ∩ B) = 8. How many students are in neither A nor B?
41 s · 18 · 21 · 8 · Universal set & Venn compl…
4. In a group of 55 students, n(A) = 26, n(B) = 29, and n(A ∩ B) = 10. How many students are in neither A nor B?
55 s · 26 · 29 · 10 · Universal set & Venn compl…
5. In a group of 30 students, n(A) = 18, n(B) = 14, and n(A ∩ B) = 8. How many students are in neither A nor B?
30 s · 18 · 14 · 8 · Universal set & Venn compl…
6. In a group of 30 students, n(A) = 18, n(B) = 8, and n(A ∩ B) = 3. How many students are in neither A nor B?
30 s · 18 · 8 · 3 · Universal set & Venn compl…
7. In a group of 28 students, n(A) = 11, n(B) = 15, and n(A ∩ B) = 6. How many students are in neither A nor B?
28 s · 11 · 15 · 6 · Universal set & Venn compl…
8. In a group of 39 students, n(A) = 8, n(B) = 16, and n(A ∩ B) = 3. How many students are in neither A nor B?
39 s · 8 · 16 · 3 · Universal set & Venn compl…
9. In a group of 43 students, n(A) = 25, n(B) = 22, and n(A ∩ B) = 11. How many students are in neither A nor B?
43 s · 25 · 22 · 11 · Universal set & Venn compl…
10. In a group of 41 students, n(A) = 17, n(B) = 19, and n(A ∩ B) = 12. How many students are in neither A nor B?
41 s · 17 · 19 · 12 · Universal set & Venn compl…
11. In a group of 30 students, n(A) = 19, n(B) = 17, and n(A ∩ B) = 10. How many students are in neither A nor B?
30 s · 19 · 17 · 10 · Universal set & Venn compl…
12. In a group of 56 students, n(A) = 29, n(B) = 32, and n(A ∩ B) = 12. How many students are in neither A nor B?
56 s · 29 · 32 · 12 · Universal set & Venn compl…

12 questions · Seed 104734 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 16-18

Universal set & Venn complements

Answers and reasoning. Review before teaching.

1. In a group of 37 students, n(A) = 14, n(B) = 25, and n(A ∩ B) = 10. How many students are in neither A nor B?
8
By inclusion-exclusion, n(A ∪ B) = 14 + 25 − 10 = 29, leaving 37 − 29 = 8 in neither set.
2. In a group of 48 students, n(A) = 32, n(B) = 16, and n(A ∩ B) = 12. How many students are in neither A nor B?
12
By inclusion-exclusion, n(A ∪ B) = 32 + 16 − 12 = 36, leaving 48 − 36 = 12 in neither set.
3. In a group of 41 students, n(A) = 18, n(B) = 21, and n(A ∩ B) = 8. How many students are in neither A nor B?
10
By inclusion-exclusion, n(A ∪ B) = 18 + 21 − 8 = 31, leaving 41 − 31 = 10 in neither set.
4. In a group of 55 students, n(A) = 26, n(B) = 29, and n(A ∩ B) = 10. How many students are in neither A nor B?
10
By inclusion-exclusion, n(A ∪ B) = 26 + 29 − 10 = 45, leaving 55 − 45 = 10 in neither set.
5. In a group of 30 students, n(A) = 18, n(B) = 14, and n(A ∩ B) = 8. How many students are in neither A nor B?
6
By inclusion-exclusion, n(A ∪ B) = 18 + 14 − 8 = 24, leaving 30 − 24 = 6 in neither set.
6. In a group of 30 students, n(A) = 18, n(B) = 8, and n(A ∩ B) = 3. How many students are in neither A nor B?
7
By inclusion-exclusion, n(A ∪ B) = 18 + 8 − 3 = 23, leaving 30 − 23 = 7 in neither set.
7. In a group of 28 students, n(A) = 11, n(B) = 15, and n(A ∩ B) = 6. How many students are in neither A nor B?
8
By inclusion-exclusion, n(A ∪ B) = 11 + 15 − 6 = 20, leaving 28 − 20 = 8 in neither set.
8. In a group of 39 students, n(A) = 8, n(B) = 16, and n(A ∩ B) = 3. How many students are in neither A nor B?
18
By inclusion-exclusion, n(A ∪ B) = 8 + 16 − 3 = 21, leaving 39 − 21 = 18 in neither set.
9. In a group of 43 students, n(A) = 25, n(B) = 22, and n(A ∩ B) = 11. How many students are in neither A nor B?
7
By inclusion-exclusion, n(A ∪ B) = 25 + 22 − 11 = 36, leaving 43 − 36 = 7 in neither set.
10. In a group of 41 students, n(A) = 17, n(B) = 19, and n(A ∩ B) = 12. How many students are in neither A nor B?
17
By inclusion-exclusion, n(A ∪ B) = 17 + 19 − 12 = 24, leaving 41 − 24 = 17 in neither set.
11. In a group of 30 students, n(A) = 19, n(B) = 17, and n(A ∩ B) = 10. How many students are in neither A nor B?
4
By inclusion-exclusion, n(A ∪ B) = 19 + 17 − 10 = 26, leaving 30 − 26 = 4 in neither set.
12. In a group of 56 students, n(A) = 29, n(B) = 32, and n(A ∩ B) = 12. How many students are in neither A nor B?
7
By inclusion-exclusion, n(A ∪ B) = 29 + 32 − 12 = 49, leaving 56 − 49 = 7 in neither set.

12 questions · Seed 104734 · Age guidance, not curriculum certification