ReasoningAges 13-15

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.

New variation Try interactive challenge Browse templates

Age band:Ages 13-15 Ages 16-18

Choose “Save as PDF” to keep a copy. Use your browser’s paper setting for A4 or Letter.

Worksheet StudioPractice pack · Ages 13-15

Universal set & Venn complements

Take your time. Show your thinking.

1. In a group of 35 students, n(A) = 12, n(B) = 22, and n(A ∩ B) = 7. How many students are in neither A nor B?
35 s · 12 · 22 · 7 · Universal set & Venn compl…
2. In a group of 33 students, n(A) = 18, n(B) = 12, and n(A ∩ B) = 2. How many students are in neither A nor B?
33 s · 18 · 12 · 2 · Universal set & Venn compl…
3. In a group of 32 students, n(A) = 13, n(B) = 6, and n(A ∩ B) = 2. How many students are in neither A nor B?
32 s · 13 · 6 · 2 · Universal set & Venn compl…
4. In a group of 51 students, n(A) = 18, n(B) = 32, and n(A ∩ B) = 12. How many students are in neither A nor B?
51 s · 18 · 32 · 12 · Universal set & Venn compl…
5. In a group of 41 students, n(A) = 19, n(B) = 30, and n(A ∩ B) = 12. How many students are in neither A nor B?
41 s · 19 · 30 · 12 · Universal set & Venn compl…
6. In a group of 33 students, n(A) = 15, n(B) = 17, and n(A ∩ B) = 2. How many students are in neither A nor B?
33 s · 15 · 17 · 2 · Universal set & Venn compl…
7. In a group of 46 students, n(A) = 25, n(B) = 15, and n(A ∩ B) = 5. How many students are in neither A nor B?
46 s · 25 · 15 · 5 · Universal set & Venn compl…
8. In a group of 35 students, n(A) = 17, n(B) = 13, and n(A ∩ B) = 2. How many students are in neither A nor B?
35 s · 17 · 13 · 2 · Universal set & Venn compl…
9. In a group of 46 students, n(A) = 20, n(B) = 18, and n(A ∩ B) = 7. How many students are in neither A nor B?
46 s · 20 · 18 · 7 · Universal set & Venn compl…
10. In a group of 30 students, n(A) = 7, n(B) = 19, and n(A ∩ B) = 2. How many students are in neither A nor B?
30 s · 7 · 19 · 2 · Universal set & Venn compl…
11. In a group of 60 students, n(A) = 29, n(B) = 25, and n(A ∩ B) = 11. How many students are in neither A nor B?
60 s · 29 · 25 · 11 · Universal set & Venn compl…
12. In a group of 59 students, n(A) = 31, n(B) = 30, and n(A ∩ B) = 12. How many students are in neither A nor B?
59 s · 31 · 30 · 12 · Universal set & Venn compl…

12 questions · Seed 44 · Age guidance, not curriculum certification

View the answer key

Worksheet StudioAnswer key · Ages 13-15

Universal set & Venn complements

Answers and reasoning. Review before teaching.

1. In a group of 35 students, n(A) = 12, n(B) = 22, and n(A ∩ B) = 7. How many students are in neither A nor B?
8
By inclusion-exclusion, n(A ∪ B) = 12 + 22 − 7 = 27, leaving 35 − 27 = 8 in neither set.
2. In a group of 33 students, n(A) = 18, n(B) = 12, and n(A ∩ B) = 2. How many students are in neither A nor B?
5
By inclusion-exclusion, n(A ∪ B) = 18 + 12 − 2 = 28, leaving 33 − 28 = 5 in neither set.
3. In a group of 32 students, n(A) = 13, n(B) = 6, and n(A ∩ B) = 2. How many students are in neither A nor B?
15
By inclusion-exclusion, n(A ∪ B) = 13 + 6 − 2 = 17, leaving 32 − 17 = 15 in neither set.
4. In a group of 51 students, n(A) = 18, n(B) = 32, and n(A ∩ B) = 12. How many students are in neither A nor B?
13
By inclusion-exclusion, n(A ∪ B) = 18 + 32 − 12 = 38, leaving 51 − 38 = 13 in neither set.
5. In a group of 41 students, n(A) = 19, n(B) = 30, and n(A ∩ B) = 12. How many students are in neither A nor B?
4
By inclusion-exclusion, n(A ∪ B) = 19 + 30 − 12 = 37, leaving 41 − 37 = 4 in neither set.
6. In a group of 33 students, n(A) = 15, n(B) = 17, and n(A ∩ B) = 2. How many students are in neither A nor B?
3
By inclusion-exclusion, n(A ∪ B) = 15 + 17 − 2 = 30, leaving 33 − 30 = 3 in neither set.
7. In a group of 46 students, n(A) = 25, n(B) = 15, and n(A ∩ B) = 5. How many students are in neither A nor B?
11
By inclusion-exclusion, n(A ∪ B) = 25 + 15 − 5 = 35, leaving 46 − 35 = 11 in neither set.
8. In a group of 35 students, n(A) = 17, n(B) = 13, and n(A ∩ B) = 2. How many students are in neither A nor B?
7
By inclusion-exclusion, n(A ∪ B) = 17 + 13 − 2 = 28, leaving 35 − 28 = 7 in neither set.
9. In a group of 46 students, n(A) = 20, n(B) = 18, and n(A ∩ B) = 7. How many students are in neither A nor B?
15
By inclusion-exclusion, n(A ∪ B) = 20 + 18 − 7 = 31, leaving 46 − 31 = 15 in neither set.
10. In a group of 30 students, n(A) = 7, n(B) = 19, and n(A ∩ B) = 2. How many students are in neither A nor B?
6
By inclusion-exclusion, n(A ∪ B) = 7 + 19 − 2 = 24, leaving 30 − 24 = 6 in neither set.
11. In a group of 60 students, n(A) = 29, n(B) = 25, and n(A ∩ B) = 11. How many students are in neither A nor B?
17
By inclusion-exclusion, n(A ∪ B) = 29 + 25 − 11 = 43, leaving 60 − 43 = 17 in neither set.
12. In a group of 59 students, n(A) = 31, n(B) = 30, and n(A ∩ B) = 12. How many students are in neither A nor B?
10
By inclusion-exclusion, n(A ∪ B) = 31 + 30 − 12 = 49, leaving 59 − 49 = 10 in neither set.

12 questions · Seed 44 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 13-15

Universal set & Venn complements

Take your time. Show your thinking.

1. In a group of 35 students, n(A) = 12, n(B) = 22, and n(A ∩ B) = 7. How many students are in neither A nor B?
35 s · 12 · 22 · 7 · Universal set & Venn compl…
2. In a group of 33 students, n(A) = 18, n(B) = 12, and n(A ∩ B) = 2. How many students are in neither A nor B?
33 s · 18 · 12 · 2 · Universal set & Venn compl…
3. In a group of 32 students, n(A) = 13, n(B) = 6, and n(A ∩ B) = 2. How many students are in neither A nor B?
32 s · 13 · 6 · 2 · Universal set & Venn compl…
4. In a group of 51 students, n(A) = 18, n(B) = 32, and n(A ∩ B) = 12. How many students are in neither A nor B?
51 s · 18 · 32 · 12 · Universal set & Venn compl…
5. In a group of 41 students, n(A) = 19, n(B) = 30, and n(A ∩ B) = 12. How many students are in neither A nor B?
41 s · 19 · 30 · 12 · Universal set & Venn compl…
6. In a group of 33 students, n(A) = 15, n(B) = 17, and n(A ∩ B) = 2. How many students are in neither A nor B?
33 s · 15 · 17 · 2 · Universal set & Venn compl…
7. In a group of 46 students, n(A) = 25, n(B) = 15, and n(A ∩ B) = 5. How many students are in neither A nor B?
46 s · 25 · 15 · 5 · Universal set & Venn compl…
8. In a group of 35 students, n(A) = 17, n(B) = 13, and n(A ∩ B) = 2. How many students are in neither A nor B?
35 s · 17 · 13 · 2 · Universal set & Venn compl…
9. In a group of 46 students, n(A) = 20, n(B) = 18, and n(A ∩ B) = 7. How many students are in neither A nor B?
46 s · 20 · 18 · 7 · Universal set & Venn compl…
10. In a group of 30 students, n(A) = 7, n(B) = 19, and n(A ∩ B) = 2. How many students are in neither A nor B?
30 s · 7 · 19 · 2 · Universal set & Venn compl…
11. In a group of 60 students, n(A) = 29, n(B) = 25, and n(A ∩ B) = 11. How many students are in neither A nor B?
60 s · 29 · 25 · 11 · Universal set & Venn compl…
12. In a group of 59 students, n(A) = 31, n(B) = 30, and n(A ∩ B) = 12. How many students are in neither A nor B?
59 s · 31 · 30 · 12 · Universal set & Venn compl…

12 questions · Seed 44 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 13-15

Universal set & Venn complements

Answers and reasoning. Review before teaching.

1. In a group of 35 students, n(A) = 12, n(B) = 22, and n(A ∩ B) = 7. How many students are in neither A nor B?
8
By inclusion-exclusion, n(A ∪ B) = 12 + 22 − 7 = 27, leaving 35 − 27 = 8 in neither set.
2. In a group of 33 students, n(A) = 18, n(B) = 12, and n(A ∩ B) = 2. How many students are in neither A nor B?
5
By inclusion-exclusion, n(A ∪ B) = 18 + 12 − 2 = 28, leaving 33 − 28 = 5 in neither set.
3. In a group of 32 students, n(A) = 13, n(B) = 6, and n(A ∩ B) = 2. How many students are in neither A nor B?
15
By inclusion-exclusion, n(A ∪ B) = 13 + 6 − 2 = 17, leaving 32 − 17 = 15 in neither set.
4. In a group of 51 students, n(A) = 18, n(B) = 32, and n(A ∩ B) = 12. How many students are in neither A nor B?
13
By inclusion-exclusion, n(A ∪ B) = 18 + 32 − 12 = 38, leaving 51 − 38 = 13 in neither set.
5. In a group of 41 students, n(A) = 19, n(B) = 30, and n(A ∩ B) = 12. How many students are in neither A nor B?
4
By inclusion-exclusion, n(A ∪ B) = 19 + 30 − 12 = 37, leaving 41 − 37 = 4 in neither set.
6. In a group of 33 students, n(A) = 15, n(B) = 17, and n(A ∩ B) = 2. How many students are in neither A nor B?
3
By inclusion-exclusion, n(A ∪ B) = 15 + 17 − 2 = 30, leaving 33 − 30 = 3 in neither set.
7. In a group of 46 students, n(A) = 25, n(B) = 15, and n(A ∩ B) = 5. How many students are in neither A nor B?
11
By inclusion-exclusion, n(A ∪ B) = 25 + 15 − 5 = 35, leaving 46 − 35 = 11 in neither set.
8. In a group of 35 students, n(A) = 17, n(B) = 13, and n(A ∩ B) = 2. How many students are in neither A nor B?
7
By inclusion-exclusion, n(A ∪ B) = 17 + 13 − 2 = 28, leaving 35 − 28 = 7 in neither set.
9. In a group of 46 students, n(A) = 20, n(B) = 18, and n(A ∩ B) = 7. How many students are in neither A nor B?
15
By inclusion-exclusion, n(A ∪ B) = 20 + 18 − 7 = 31, leaving 46 − 31 = 15 in neither set.
10. In a group of 30 students, n(A) = 7, n(B) = 19, and n(A ∩ B) = 2. How many students are in neither A nor B?
6
By inclusion-exclusion, n(A ∪ B) = 7 + 19 − 2 = 24, leaving 30 − 24 = 6 in neither set.
11. In a group of 60 students, n(A) = 29, n(B) = 25, and n(A ∩ B) = 11. How many students are in neither A nor B?
17
By inclusion-exclusion, n(A ∪ B) = 29 + 25 − 11 = 43, leaving 60 − 43 = 17 in neither set.
12. In a group of 59 students, n(A) = 31, n(B) = 30, and n(A ∩ B) = 12. How many students are in neither A nor B?
10
By inclusion-exclusion, n(A ∪ B) = 31 + 30 − 12 = 49, leaving 59 − 49 = 10 in neither set.

12 questions · Seed 44 · Age guidance, not curriculum certification