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 27 students, n(A) = 9, n(B) = 17, and n(A ∩ B) = 5. How many students are in neither A nor B?
27 s · 9 · 17 · 5 · Universal set & Venn compl…
2. In a group of 41 students, n(A) = 30, n(B) = 20, and n(A ∩ B) = 12. How many students are in neither A nor B?
41 s · 30 · 20 · 12 · Universal set & Venn compl…
3. In a group of 48 students, n(A) = 21, n(B) = 14, and n(A ∩ B) = 5. How many students are in neither A nor B?
48 s · 21 · 14 · 5 · Universal set & Venn compl…
4. In a group of 44 students, n(A) = 21, n(B) = 11, and n(A ∩ B) = 6. How many students are in neither A nor B?
44 s · 21 · 11 · 6 · Universal set & Venn compl…
5. In a group of 35 students, n(A) = 22, n(B) = 8, and n(A ∩ B) = 3. How many students are in neither A nor B?
35 s · 22 · 8 · 3 · Universal set & Venn compl…
6. In a group of 29 students, n(A) = 10, n(B) = 8, and n(A ∩ B) = 3. How many students are in neither A nor B?
29 s · 10 · 8 · 3 · Universal set & Venn compl…
7. In a group of 51 students, n(A) = 22, n(B) = 25, and n(A ∩ B) = 6. How many students are in neither A nor B?
51 s · 22 · 25 · 6 · Universal set & Venn compl…
8. In a group of 48 students, n(A) = 17, n(B) = 22, and n(A ∩ B) = 2. How many students are in neither A nor B?
48 s · 17 · 22 · 2 · Universal set & Venn compl…
9. In a group of 55 students, n(A) = 24, n(B) = 22, and n(A ∩ B) = 4. How many students are in neither A nor B?
55 s · 24 · 22 · 4 · Universal set & Venn compl…
10. In a group of 55 students, n(A) = 30, n(B) = 20, and n(A ∩ B) = 10. How many students are in neither A nor B?
55 s · 30 · 20 · 10 · Universal set & Venn compl…
11. In a group of 41 students, n(A) = 12, n(B) = 17, and n(A ∩ B) = 3. How many students are in neither A nor B?
41 s · 12 · 17 · 3 · Universal set & Venn compl…
12. In a group of 39 students, n(A) = 16, n(B) = 22, and n(A ∩ B) = 5. How many students are in neither A nor B?
39 s · 16 · 22 · 5 · Universal set & Venn compl…

12 questions · Seed 50 · 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 27 students, n(A) = 9, n(B) = 17, and n(A ∩ B) = 5. How many students are in neither A nor B?
6
By inclusion-exclusion, n(A ∪ B) = 9 + 17 − 5 = 21, leaving 27 − 21 = 6 in neither set.
2. In a group of 41 students, n(A) = 30, n(B) = 20, and n(A ∩ B) = 12. How many students are in neither A nor B?
3
By inclusion-exclusion, n(A ∪ B) = 30 + 20 − 12 = 38, leaving 41 − 38 = 3 in neither set.
3. In a group of 48 students, n(A) = 21, n(B) = 14, and n(A ∩ B) = 5. How many students are in neither A nor B?
18
By inclusion-exclusion, n(A ∪ B) = 21 + 14 − 5 = 30, leaving 48 − 30 = 18 in neither set.
4. In a group of 44 students, n(A) = 21, n(B) = 11, and n(A ∩ B) = 6. How many students are in neither A nor B?
18
By inclusion-exclusion, n(A ∪ B) = 21 + 11 − 6 = 26, leaving 44 − 26 = 18 in neither set.
5. In a group of 35 students, n(A) = 22, n(B) = 8, and n(A ∩ B) = 3. How many students are in neither A nor B?
8
By inclusion-exclusion, n(A ∪ B) = 22 + 8 − 3 = 27, leaving 35 − 27 = 8 in neither set.
6. In a group of 29 students, n(A) = 10, n(B) = 8, and n(A ∩ B) = 3. How many students are in neither A nor B?
14
By inclusion-exclusion, n(A ∪ B) = 10 + 8 − 3 = 15, leaving 29 − 15 = 14 in neither set.
7. In a group of 51 students, n(A) = 22, n(B) = 25, and n(A ∩ B) = 6. How many students are in neither A nor B?
10
By inclusion-exclusion, n(A ∪ B) = 22 + 25 − 6 = 41, leaving 51 − 41 = 10 in neither set.
8. In a group of 48 students, n(A) = 17, n(B) = 22, and n(A ∩ B) = 2. How many students are in neither A nor B?
11
By inclusion-exclusion, n(A ∪ B) = 17 + 22 − 2 = 37, leaving 48 − 37 = 11 in neither set.
9. In a group of 55 students, n(A) = 24, n(B) = 22, and n(A ∩ B) = 4. How many students are in neither A nor B?
13
By inclusion-exclusion, n(A ∪ B) = 24 + 22 − 4 = 42, leaving 55 − 42 = 13 in neither set.
10. In a group of 55 students, n(A) = 30, n(B) = 20, and n(A ∩ B) = 10. How many students are in neither A nor B?
15
By inclusion-exclusion, n(A ∪ B) = 30 + 20 − 10 = 40, leaving 55 − 40 = 15 in neither set.
11. In a group of 41 students, n(A) = 12, n(B) = 17, and n(A ∩ B) = 3. How many students are in neither A nor B?
15
By inclusion-exclusion, n(A ∪ B) = 12 + 17 − 3 = 26, leaving 41 − 26 = 15 in neither set.
12. In a group of 39 students, n(A) = 16, n(B) = 22, and n(A ∩ B) = 5. How many students are in neither A nor B?
6
By inclusion-exclusion, n(A ∪ B) = 16 + 22 − 5 = 33, leaving 39 − 33 = 6 in neither set.

12 questions · Seed 50 · 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 27 students, n(A) = 9, n(B) = 17, and n(A ∩ B) = 5. How many students are in neither A nor B?
27 s · 9 · 17 · 5 · Universal set & Venn compl…
2. In a group of 41 students, n(A) = 30, n(B) = 20, and n(A ∩ B) = 12. How many students are in neither A nor B?
41 s · 30 · 20 · 12 · Universal set & Venn compl…
3. In a group of 48 students, n(A) = 21, n(B) = 14, and n(A ∩ B) = 5. How many students are in neither A nor B?
48 s · 21 · 14 · 5 · Universal set & Venn compl…
4. In a group of 44 students, n(A) = 21, n(B) = 11, and n(A ∩ B) = 6. How many students are in neither A nor B?
44 s · 21 · 11 · 6 · Universal set & Venn compl…
5. In a group of 35 students, n(A) = 22, n(B) = 8, and n(A ∩ B) = 3. How many students are in neither A nor B?
35 s · 22 · 8 · 3 · Universal set & Venn compl…
6. In a group of 29 students, n(A) = 10, n(B) = 8, and n(A ∩ B) = 3. How many students are in neither A nor B?
29 s · 10 · 8 · 3 · Universal set & Venn compl…
7. In a group of 51 students, n(A) = 22, n(B) = 25, and n(A ∩ B) = 6. How many students are in neither A nor B?
51 s · 22 · 25 · 6 · Universal set & Venn compl…
8. In a group of 48 students, n(A) = 17, n(B) = 22, and n(A ∩ B) = 2. How many students are in neither A nor B?
48 s · 17 · 22 · 2 · Universal set & Venn compl…
9. In a group of 55 students, n(A) = 24, n(B) = 22, and n(A ∩ B) = 4. How many students are in neither A nor B?
55 s · 24 · 22 · 4 · Universal set & Venn compl…
10. In a group of 55 students, n(A) = 30, n(B) = 20, and n(A ∩ B) = 10. How many students are in neither A nor B?
55 s · 30 · 20 · 10 · Universal set & Venn compl…
11. In a group of 41 students, n(A) = 12, n(B) = 17, and n(A ∩ B) = 3. How many students are in neither A nor B?
41 s · 12 · 17 · 3 · Universal set & Venn compl…
12. In a group of 39 students, n(A) = 16, n(B) = 22, and n(A ∩ B) = 5. How many students are in neither A nor B?
39 s · 16 · 22 · 5 · Universal set & Venn compl…

12 questions · Seed 50 · 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 27 students, n(A) = 9, n(B) = 17, and n(A ∩ B) = 5. How many students are in neither A nor B?
6
By inclusion-exclusion, n(A ∪ B) = 9 + 17 − 5 = 21, leaving 27 − 21 = 6 in neither set.
2. In a group of 41 students, n(A) = 30, n(B) = 20, and n(A ∩ B) = 12. How many students are in neither A nor B?
3
By inclusion-exclusion, n(A ∪ B) = 30 + 20 − 12 = 38, leaving 41 − 38 = 3 in neither set.
3. In a group of 48 students, n(A) = 21, n(B) = 14, and n(A ∩ B) = 5. How many students are in neither A nor B?
18
By inclusion-exclusion, n(A ∪ B) = 21 + 14 − 5 = 30, leaving 48 − 30 = 18 in neither set.
4. In a group of 44 students, n(A) = 21, n(B) = 11, and n(A ∩ B) = 6. How many students are in neither A nor B?
18
By inclusion-exclusion, n(A ∪ B) = 21 + 11 − 6 = 26, leaving 44 − 26 = 18 in neither set.
5. In a group of 35 students, n(A) = 22, n(B) = 8, and n(A ∩ B) = 3. How many students are in neither A nor B?
8
By inclusion-exclusion, n(A ∪ B) = 22 + 8 − 3 = 27, leaving 35 − 27 = 8 in neither set.
6. In a group of 29 students, n(A) = 10, n(B) = 8, and n(A ∩ B) = 3. How many students are in neither A nor B?
14
By inclusion-exclusion, n(A ∪ B) = 10 + 8 − 3 = 15, leaving 29 − 15 = 14 in neither set.
7. In a group of 51 students, n(A) = 22, n(B) = 25, and n(A ∩ B) = 6. How many students are in neither A nor B?
10
By inclusion-exclusion, n(A ∪ B) = 22 + 25 − 6 = 41, leaving 51 − 41 = 10 in neither set.
8. In a group of 48 students, n(A) = 17, n(B) = 22, and n(A ∩ B) = 2. How many students are in neither A nor B?
11
By inclusion-exclusion, n(A ∪ B) = 17 + 22 − 2 = 37, leaving 48 − 37 = 11 in neither set.
9. In a group of 55 students, n(A) = 24, n(B) = 22, and n(A ∩ B) = 4. How many students are in neither A nor B?
13
By inclusion-exclusion, n(A ∪ B) = 24 + 22 − 4 = 42, leaving 55 − 42 = 13 in neither set.
10. In a group of 55 students, n(A) = 30, n(B) = 20, and n(A ∩ B) = 10. How many students are in neither A nor B?
15
By inclusion-exclusion, n(A ∪ B) = 30 + 20 − 10 = 40, leaving 55 − 40 = 15 in neither set.
11. In a group of 41 students, n(A) = 12, n(B) = 17, and n(A ∩ B) = 3. How many students are in neither A nor B?
15
By inclusion-exclusion, n(A ∪ B) = 12 + 17 − 3 = 26, leaving 41 − 26 = 15 in neither set.
12. In a group of 39 students, n(A) = 16, n(B) = 22, and n(A ∩ B) = 5. How many students are in neither A nor B?
6
By inclusion-exclusion, n(A ∪ B) = 16 + 22 − 5 = 33, leaving 39 − 33 = 6 in neither set.

12 questions · Seed 50 · Age guidance, not curriculum certification