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 46 students, n(A) = 16, n(B) = 20, and n(A ∩ B) = 8. How many students are in neither A nor B?
46 s · 16 · 20 · 8 · Universal set & Venn compl…
2. In a group of 41 students, n(A) = 24, n(B) = 16, and n(A ∩ B) = 11. How many students are in neither A nor B?
41 s · 24 · 16 · 11 · Universal set & Venn compl…
3. In a group of 33 students, n(A) = 8, n(B) = 12, and n(A ∩ B) = 3. How many students are in neither A nor B?
33 s · 8 · 12 · 3 · Universal set & Venn compl…
4. In a group of 25 students, n(A) = 16, n(B) = 12, and n(A ∩ B) = 8. How many students are in neither A nor B?
25 s · 16 · 12 · 8 · Universal set & Venn compl…
5. In a group of 45 students, n(A) = 26, n(B) = 25, and n(A ∩ B) = 11. How many students are in neither A nor B?
45 s · 26 · 25 · 11 · Universal set & Venn compl…
6. In a group of 43 students, n(A) = 20, n(B) = 31, and n(A ∩ B) = 12. How many students are in neither A nor B?
43 s · 20 · 31 · 12 · Universal set & Venn compl…
7. In a group of 33 students, n(A) = 17, n(B) = 12, and n(A ∩ B) = 4. How many students are in neither A nor B?
33 s · 17 · 12 · 4 · Universal set & Venn compl…
8. In a group of 37 students, n(A) = 9, n(B) = 21, and n(A ∩ B) = 5. How many students are in neither A nor B?
37 s · 9 · 21 · 5 · Universal set & Venn compl…
9. In a group of 37 students, n(A) = 18, n(B) = 21, and n(A ∩ B) = 10. How many students are in neither A nor B?
37 s · 18 · 21 · 10 · Universal set & Venn compl…
10. In a group of 30 students, n(A) = 13, n(B) = 9, and n(A ∩ B) = 5. How many students are in neither A nor B?
30 s · 13 · 9 · 5 · Universal set & Venn compl…
11. In a group of 56 students, n(A) = 26, n(B) = 23, and n(A ∩ B) = 9. How many students are in neither A nor B?
56 s · 26 · 23 · 9 · Universal set & Venn compl…
12. In a group of 38 students, n(A) = 12, n(B) = 26, and n(A ∩ B) = 6. How many students are in neither A nor B?
38 s · 12 · 26 · 6 · Universal set & Venn compl…

12 questions · Seed 104730 · 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 46 students, n(A) = 16, n(B) = 20, and n(A ∩ B) = 8. How many students are in neither A nor B?
18
By inclusion-exclusion, n(A ∪ B) = 16 + 20 − 8 = 28, leaving 46 − 28 = 18 in neither set.
2. In a group of 41 students, n(A) = 24, n(B) = 16, and n(A ∩ B) = 11. How many students are in neither A nor B?
12
By inclusion-exclusion, n(A ∪ B) = 24 + 16 − 11 = 29, leaving 41 − 29 = 12 in neither set.
3. In a group of 33 students, n(A) = 8, n(B) = 12, and n(A ∩ B) = 3. How many students are in neither A nor B?
16
By inclusion-exclusion, n(A ∪ B) = 8 + 12 − 3 = 17, leaving 33 − 17 = 16 in neither set.
4. In a group of 25 students, n(A) = 16, n(B) = 12, and n(A ∩ B) = 8. How many students are in neither A nor B?
5
By inclusion-exclusion, n(A ∪ B) = 16 + 12 − 8 = 20, leaving 25 − 20 = 5 in neither set.
5. In a group of 45 students, n(A) = 26, n(B) = 25, and n(A ∩ B) = 11. How many students are in neither A nor B?
5
By inclusion-exclusion, n(A ∪ B) = 26 + 25 − 11 = 40, leaving 45 − 40 = 5 in neither set.
6. In a group of 43 students, n(A) = 20, n(B) = 31, and n(A ∩ B) = 12. How many students are in neither A nor B?
4
By inclusion-exclusion, n(A ∪ B) = 20 + 31 − 12 = 39, leaving 43 − 39 = 4 in neither set.
7. In a group of 33 students, n(A) = 17, n(B) = 12, and n(A ∩ B) = 4. How many students are in neither A nor B?
8
By inclusion-exclusion, n(A ∪ B) = 17 + 12 − 4 = 25, leaving 33 − 25 = 8 in neither set.
8. In a group of 37 students, n(A) = 9, n(B) = 21, and n(A ∩ B) = 5. How many students are in neither A nor B?
12
By inclusion-exclusion, n(A ∪ B) = 9 + 21 − 5 = 25, leaving 37 − 25 = 12 in neither set.
9. In a group of 37 students, n(A) = 18, n(B) = 21, and n(A ∩ B) = 10. How many students are in neither A nor B?
8
By inclusion-exclusion, n(A ∪ B) = 18 + 21 − 10 = 29, leaving 37 − 29 = 8 in neither set.
10. In a group of 30 students, n(A) = 13, n(B) = 9, and n(A ∩ B) = 5. How many students are in neither A nor B?
13
By inclusion-exclusion, n(A ∪ B) = 13 + 9 − 5 = 17, leaving 30 − 17 = 13 in neither set.
11. In a group of 56 students, n(A) = 26, n(B) = 23, and n(A ∩ B) = 9. How many students are in neither A nor B?
16
By inclusion-exclusion, n(A ∪ B) = 26 + 23 − 9 = 40, leaving 56 − 40 = 16 in neither set.
12. In a group of 38 students, n(A) = 12, n(B) = 26, and n(A ∩ B) = 6. How many students are in neither A nor B?
6
By inclusion-exclusion, n(A ∪ B) = 12 + 26 − 6 = 32, leaving 38 − 32 = 6 in neither set.

12 questions · Seed 104730 · 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 46 students, n(A) = 16, n(B) = 20, and n(A ∩ B) = 8. How many students are in neither A nor B?
46 s · 16 · 20 · 8 · Universal set & Venn compl…
2. In a group of 41 students, n(A) = 24, n(B) = 16, and n(A ∩ B) = 11. How many students are in neither A nor B?
41 s · 24 · 16 · 11 · Universal set & Venn compl…
3. In a group of 33 students, n(A) = 8, n(B) = 12, and n(A ∩ B) = 3. How many students are in neither A nor B?
33 s · 8 · 12 · 3 · Universal set & Venn compl…
4. In a group of 25 students, n(A) = 16, n(B) = 12, and n(A ∩ B) = 8. How many students are in neither A nor B?
25 s · 16 · 12 · 8 · Universal set & Venn compl…
5. In a group of 45 students, n(A) = 26, n(B) = 25, and n(A ∩ B) = 11. How many students are in neither A nor B?
45 s · 26 · 25 · 11 · Universal set & Venn compl…
6. In a group of 43 students, n(A) = 20, n(B) = 31, and n(A ∩ B) = 12. How many students are in neither A nor B?
43 s · 20 · 31 · 12 · Universal set & Venn compl…
7. In a group of 33 students, n(A) = 17, n(B) = 12, and n(A ∩ B) = 4. How many students are in neither A nor B?
33 s · 17 · 12 · 4 · Universal set & Venn compl…
8. In a group of 37 students, n(A) = 9, n(B) = 21, and n(A ∩ B) = 5. How many students are in neither A nor B?
37 s · 9 · 21 · 5 · Universal set & Venn compl…
9. In a group of 37 students, n(A) = 18, n(B) = 21, and n(A ∩ B) = 10. How many students are in neither A nor B?
37 s · 18 · 21 · 10 · Universal set & Venn compl…
10. In a group of 30 students, n(A) = 13, n(B) = 9, and n(A ∩ B) = 5. How many students are in neither A nor B?
30 s · 13 · 9 · 5 · Universal set & Venn compl…
11. In a group of 56 students, n(A) = 26, n(B) = 23, and n(A ∩ B) = 9. How many students are in neither A nor B?
56 s · 26 · 23 · 9 · Universal set & Venn compl…
12. In a group of 38 students, n(A) = 12, n(B) = 26, and n(A ∩ B) = 6. How many students are in neither A nor B?
38 s · 12 · 26 · 6 · Universal set & Venn compl…

12 questions · Seed 104730 · 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 46 students, n(A) = 16, n(B) = 20, and n(A ∩ B) = 8. How many students are in neither A nor B?
18
By inclusion-exclusion, n(A ∪ B) = 16 + 20 − 8 = 28, leaving 46 − 28 = 18 in neither set.
2. In a group of 41 students, n(A) = 24, n(B) = 16, and n(A ∩ B) = 11. How many students are in neither A nor B?
12
By inclusion-exclusion, n(A ∪ B) = 24 + 16 − 11 = 29, leaving 41 − 29 = 12 in neither set.
3. In a group of 33 students, n(A) = 8, n(B) = 12, and n(A ∩ B) = 3. How many students are in neither A nor B?
16
By inclusion-exclusion, n(A ∪ B) = 8 + 12 − 3 = 17, leaving 33 − 17 = 16 in neither set.
4. In a group of 25 students, n(A) = 16, n(B) = 12, and n(A ∩ B) = 8. How many students are in neither A nor B?
5
By inclusion-exclusion, n(A ∪ B) = 16 + 12 − 8 = 20, leaving 25 − 20 = 5 in neither set.
5. In a group of 45 students, n(A) = 26, n(B) = 25, and n(A ∩ B) = 11. How many students are in neither A nor B?
5
By inclusion-exclusion, n(A ∪ B) = 26 + 25 − 11 = 40, leaving 45 − 40 = 5 in neither set.
6. In a group of 43 students, n(A) = 20, n(B) = 31, and n(A ∩ B) = 12. How many students are in neither A nor B?
4
By inclusion-exclusion, n(A ∪ B) = 20 + 31 − 12 = 39, leaving 43 − 39 = 4 in neither set.
7. In a group of 33 students, n(A) = 17, n(B) = 12, and n(A ∩ B) = 4. How many students are in neither A nor B?
8
By inclusion-exclusion, n(A ∪ B) = 17 + 12 − 4 = 25, leaving 33 − 25 = 8 in neither set.
8. In a group of 37 students, n(A) = 9, n(B) = 21, and n(A ∩ B) = 5. How many students are in neither A nor B?
12
By inclusion-exclusion, n(A ∪ B) = 9 + 21 − 5 = 25, leaving 37 − 25 = 12 in neither set.
9. In a group of 37 students, n(A) = 18, n(B) = 21, and n(A ∩ B) = 10. How many students are in neither A nor B?
8
By inclusion-exclusion, n(A ∪ B) = 18 + 21 − 10 = 29, leaving 37 − 29 = 8 in neither set.
10. In a group of 30 students, n(A) = 13, n(B) = 9, and n(A ∩ B) = 5. How many students are in neither A nor B?
13
By inclusion-exclusion, n(A ∪ B) = 13 + 9 − 5 = 17, leaving 30 − 17 = 13 in neither set.
11. In a group of 56 students, n(A) = 26, n(B) = 23, and n(A ∩ B) = 9. How many students are in neither A nor B?
16
By inclusion-exclusion, n(A ∪ B) = 26 + 23 − 9 = 40, leaving 56 − 40 = 16 in neither set.
12. In a group of 38 students, n(A) = 12, n(B) = 26, and n(A ∩ B) = 6. How many students are in neither A nor B?
6
By inclusion-exclusion, n(A ∪ B) = 12 + 26 − 6 = 32, leaving 38 − 32 = 6 in neither set.

12 questions · Seed 104730 · Age guidance, not curriculum certification