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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Worksheet StudioPractice pack · Ages 16-18

Universal set & Venn complements

Take your time. Show your thinking.

1. In a group of 44 students, n(A) = 18, n(B) = 31, and n(A ∩ B) = 11. How many students are in neither A nor B?
44 s · 18 · 31 · 11 · Universal set & Venn compl…
2. In a group of 46 students, n(A) = 16, n(B) = 21, and n(A ∩ B) = 9. How many students are in neither A nor B?
46 s · 16 · 21 · 9 · Universal set & Venn compl…
3. In a group of 21 students, n(A) = 12, n(B) = 13, and n(A ∩ B) = 7. How many students are in neither A nor B?
21 s · 12 · 13 · 7 · Universal set & Venn compl…
4. In a group of 23 students, n(A) = 15, n(B) = 16, and n(A ∩ B) = 11. How many students are in neither A nor B?
23 s · 15 · 16 · 11 · Universal set & Venn compl…
5. In a group of 39 students, n(A) = 19, n(B) = 26, and n(A ∩ B) = 9. How many students are in neither A nor B?
39 s · 19 · 26 · 9 · Universal set & Venn compl…
6. In a group of 49 students, n(A) = 22, n(B) = 22, and n(A ∩ B) = 5. How many students are in neither A nor B?
49 s · 22 · 22 · 5 · Universal set & Venn compl…
7. In a group of 37 students, n(A) = 17, n(B) = 13, and n(A ∩ B) = 8. How many students are in neither A nor B?
37 s · 17 · 13 · 8 · Universal set & Venn compl…
8. In a group of 36 students, n(A) = 25, n(B) = 13, and n(A ∩ B) = 8. How many students are in neither A nor B?
36 s · 25 · 13 · 8 · Universal set & Venn compl…
9. In a group of 47 students, n(A) = 10, n(B) = 21, and n(A ∩ B) = 2. How many students are in neither A nor B?
47 s · 10 · 21 · 2 · Universal set & Venn compl…
10. In a group of 35 students, n(A) = 19, n(B) = 7, and n(A ∩ B) = 2. How many students are in neither A nor B?
35 s · 19 · 7 · 2 · Universal set & Venn compl…
11. In a group of 30 students, n(A) = 23, n(B) = 14, and n(A ∩ B) = 10. How many students are in neither A nor B?
30 s · 23 · 14 · 10 · Universal set & Venn compl…
12. In a group of 38 students, n(A) = 14, n(B) = 14, and n(A ∩ B) = 7. How many students are in neither A nor B?
38 s · 14 · 14 · 7 · Universal set & Venn compl…

12 questions · Seed 45 · 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 44 students, n(A) = 18, n(B) = 31, and n(A ∩ B) = 11. How many students are in neither A nor B?
6
By inclusion-exclusion, n(A ∪ B) = 18 + 31 − 11 = 38, leaving 44 − 38 = 6 in neither set.
2. In a group of 46 students, n(A) = 16, n(B) = 21, and n(A ∩ B) = 9. How many students are in neither A nor B?
18
By inclusion-exclusion, n(A ∪ B) = 16 + 21 − 9 = 28, leaving 46 − 28 = 18 in neither set.
3. In a group of 21 students, n(A) = 12, n(B) = 13, and n(A ∩ B) = 7. How many students are in neither A nor B?
3
By inclusion-exclusion, n(A ∪ B) = 12 + 13 − 7 = 18, leaving 21 − 18 = 3 in neither set.
4. In a group of 23 students, n(A) = 15, n(B) = 16, and n(A ∩ B) = 11. How many students are in neither A nor B?
3
By inclusion-exclusion, n(A ∪ B) = 15 + 16 − 11 = 20, leaving 23 − 20 = 3 in neither set.
5. In a group of 39 students, n(A) = 19, n(B) = 26, and n(A ∩ B) = 9. How many students are in neither A nor B?
3
By inclusion-exclusion, n(A ∪ B) = 19 + 26 − 9 = 36, leaving 39 − 36 = 3 in neither set.
6. In a group of 49 students, n(A) = 22, n(B) = 22, and n(A ∩ B) = 5. How many students are in neither A nor B?
10
By inclusion-exclusion, n(A ∪ B) = 22 + 22 − 5 = 39, leaving 49 − 39 = 10 in neither set.
7. In a group of 37 students, n(A) = 17, n(B) = 13, and n(A ∩ B) = 8. How many students are in neither A nor B?
15
By inclusion-exclusion, n(A ∪ B) = 17 + 13 − 8 = 22, leaving 37 − 22 = 15 in neither set.
8. In a group of 36 students, n(A) = 25, n(B) = 13, and n(A ∩ B) = 8. How many students are in neither A nor B?
6
By inclusion-exclusion, n(A ∪ B) = 25 + 13 − 8 = 30, leaving 36 − 30 = 6 in neither set.
9. In a group of 47 students, n(A) = 10, n(B) = 21, and n(A ∩ B) = 2. How many students are in neither A nor B?
18
By inclusion-exclusion, n(A ∪ B) = 10 + 21 − 2 = 29, leaving 47 − 29 = 18 in neither set.
10. In a group of 35 students, n(A) = 19, n(B) = 7, and n(A ∩ B) = 2. How many students are in neither A nor B?
11
By inclusion-exclusion, n(A ∪ B) = 19 + 7 − 2 = 24, leaving 35 − 24 = 11 in neither set.
11. In a group of 30 students, n(A) = 23, n(B) = 14, and n(A ∩ B) = 10. How many students are in neither A nor B?
3
By inclusion-exclusion, n(A ∪ B) = 23 + 14 − 10 = 27, leaving 30 − 27 = 3 in neither set.
12. In a group of 38 students, n(A) = 14, n(B) = 14, and n(A ∩ B) = 7. How many students are in neither A nor B?
17
By inclusion-exclusion, n(A ∪ B) = 14 + 14 − 7 = 21, leaving 38 − 21 = 17 in neither set.

12 questions · Seed 45 · 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 44 students, n(A) = 18, n(B) = 31, and n(A ∩ B) = 11. How many students are in neither A nor B?
44 s · 18 · 31 · 11 · Universal set & Venn compl…
2. In a group of 46 students, n(A) = 16, n(B) = 21, and n(A ∩ B) = 9. How many students are in neither A nor B?
46 s · 16 · 21 · 9 · Universal set & Venn compl…
3. In a group of 21 students, n(A) = 12, n(B) = 13, and n(A ∩ B) = 7. How many students are in neither A nor B?
21 s · 12 · 13 · 7 · Universal set & Venn compl…
4. In a group of 23 students, n(A) = 15, n(B) = 16, and n(A ∩ B) = 11. How many students are in neither A nor B?
23 s · 15 · 16 · 11 · Universal set & Venn compl…
5. In a group of 39 students, n(A) = 19, n(B) = 26, and n(A ∩ B) = 9. How many students are in neither A nor B?
39 s · 19 · 26 · 9 · Universal set & Venn compl…
6. In a group of 49 students, n(A) = 22, n(B) = 22, and n(A ∩ B) = 5. How many students are in neither A nor B?
49 s · 22 · 22 · 5 · Universal set & Venn compl…
7. In a group of 37 students, n(A) = 17, n(B) = 13, and n(A ∩ B) = 8. How many students are in neither A nor B?
37 s · 17 · 13 · 8 · Universal set & Venn compl…
8. In a group of 36 students, n(A) = 25, n(B) = 13, and n(A ∩ B) = 8. How many students are in neither A nor B?
36 s · 25 · 13 · 8 · Universal set & Venn compl…
9. In a group of 47 students, n(A) = 10, n(B) = 21, and n(A ∩ B) = 2. How many students are in neither A nor B?
47 s · 10 · 21 · 2 · Universal set & Venn compl…
10. In a group of 35 students, n(A) = 19, n(B) = 7, and n(A ∩ B) = 2. How many students are in neither A nor B?
35 s · 19 · 7 · 2 · Universal set & Venn compl…
11. In a group of 30 students, n(A) = 23, n(B) = 14, and n(A ∩ B) = 10. How many students are in neither A nor B?
30 s · 23 · 14 · 10 · Universal set & Venn compl…
12. In a group of 38 students, n(A) = 14, n(B) = 14, and n(A ∩ B) = 7. How many students are in neither A nor B?
38 s · 14 · 14 · 7 · Universal set & Venn compl…

12 questions · Seed 45 · 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 44 students, n(A) = 18, n(B) = 31, and n(A ∩ B) = 11. How many students are in neither A nor B?
6
By inclusion-exclusion, n(A ∪ B) = 18 + 31 − 11 = 38, leaving 44 − 38 = 6 in neither set.
2. In a group of 46 students, n(A) = 16, n(B) = 21, and n(A ∩ B) = 9. How many students are in neither A nor B?
18
By inclusion-exclusion, n(A ∪ B) = 16 + 21 − 9 = 28, leaving 46 − 28 = 18 in neither set.
3. In a group of 21 students, n(A) = 12, n(B) = 13, and n(A ∩ B) = 7. How many students are in neither A nor B?
3
By inclusion-exclusion, n(A ∪ B) = 12 + 13 − 7 = 18, leaving 21 − 18 = 3 in neither set.
4. In a group of 23 students, n(A) = 15, n(B) = 16, and n(A ∩ B) = 11. How many students are in neither A nor B?
3
By inclusion-exclusion, n(A ∪ B) = 15 + 16 − 11 = 20, leaving 23 − 20 = 3 in neither set.
5. In a group of 39 students, n(A) = 19, n(B) = 26, and n(A ∩ B) = 9. How many students are in neither A nor B?
3
By inclusion-exclusion, n(A ∪ B) = 19 + 26 − 9 = 36, leaving 39 − 36 = 3 in neither set.
6. In a group of 49 students, n(A) = 22, n(B) = 22, and n(A ∩ B) = 5. How many students are in neither A nor B?
10
By inclusion-exclusion, n(A ∪ B) = 22 + 22 − 5 = 39, leaving 49 − 39 = 10 in neither set.
7. In a group of 37 students, n(A) = 17, n(B) = 13, and n(A ∩ B) = 8. How many students are in neither A nor B?
15
By inclusion-exclusion, n(A ∪ B) = 17 + 13 − 8 = 22, leaving 37 − 22 = 15 in neither set.
8. In a group of 36 students, n(A) = 25, n(B) = 13, and n(A ∩ B) = 8. How many students are in neither A nor B?
6
By inclusion-exclusion, n(A ∪ B) = 25 + 13 − 8 = 30, leaving 36 − 30 = 6 in neither set.
9. In a group of 47 students, n(A) = 10, n(B) = 21, and n(A ∩ B) = 2. How many students are in neither A nor B?
18
By inclusion-exclusion, n(A ∪ B) = 10 + 21 − 2 = 29, leaving 47 − 29 = 18 in neither set.
10. In a group of 35 students, n(A) = 19, n(B) = 7, and n(A ∩ B) = 2. How many students are in neither A nor B?
11
By inclusion-exclusion, n(A ∪ B) = 19 + 7 − 2 = 24, leaving 35 − 24 = 11 in neither set.
11. In a group of 30 students, n(A) = 23, n(B) = 14, and n(A ∩ B) = 10. How many students are in neither A nor B?
3
By inclusion-exclusion, n(A ∪ B) = 23 + 14 − 10 = 27, leaving 30 − 27 = 3 in neither set.
12. In a group of 38 students, n(A) = 14, n(B) = 14, and n(A ∩ B) = 7. How many students are in neither A nor B?
17
By inclusion-exclusion, n(A ∪ B) = 14 + 14 − 7 = 21, leaving 38 − 21 = 17 in neither set.

12 questions · Seed 45 · Age guidance, not curriculum certification