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.

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 16-18

Universal set & Venn complements

Take your time. Show your thinking.

1. In a group of 47 students, n(A) = 18, n(B) = 19, and n(A ∩ B) = 7. How many students are in neither A nor B?
47 s · 18 · 19 · 7 · Universal set & Venn compl…
2. In a group of 44 students, n(A) = 17, n(B) = 24, and n(A ∩ B) = 8. How many students are in neither A nor B?
44 s · 17 · 24 · 8 · Universal set & Venn compl…
3. In a group of 60 students, n(A) = 23, n(B) = 28, and n(A ∩ B) = 9. How many students are in neither A nor B?
60 s · 23 · 28 · 9 · Universal set & Venn compl…
4. In a group of 39 students, n(A) = 12, n(B) = 16, and n(A ∩ B) = 7. How many students are in neither A nor B?
39 s · 12 · 16 · 7 · Universal set & Venn compl…
5. In a group of 33 students, n(A) = 11, n(B) = 15, and n(A ∩ B) = 7. How many students are in neither A nor B?
33 s · 11 · 15 · 7 · Universal set & Venn compl…
6. In a group of 28 students, n(A) = 11, n(B) = 14, and n(A ∩ B) = 5. How many students are in neither A nor B?
28 s · 11 · 14 · 5 · Universal set & Venn compl…
7. In a group of 28 students, n(A) = 20, n(B) = 11, and n(A ∩ B) = 6. How many students are in neither A nor B?
28 s · 20 · 11 · 6 · Universal set & Venn compl…
8. In a group of 43 students, n(A) = 20, n(B) = 19, and n(A ∩ B) = 11. How many students are in neither A nor B?
43 s · 20 · 19 · 11 · Universal set & Venn compl…
9. In a group of 38 students, n(A) = 12, n(B) = 25, and n(A ∩ B) = 7. How many students are in neither A nor B?
38 s · 12 · 25 · 7 · Universal set & Venn compl…
10. In a group of 57 students, n(A) = 20, n(B) = 28, and n(A ∩ B) = 9. How many students are in neither A nor B?
57 s · 20 · 28 · 9 · Universal set & Venn compl…
11. In a group of 51 students, n(A) = 15, n(B) = 29, and n(A ∩ B) = 10. How many students are in neither A nor B?
51 s · 15 · 29 · 10 · Universal set & Venn compl…
12. In a group of 32 students, n(A) = 15, n(B) = 13, and n(A ∩ B) = 7. How many students are in neither A nor B?
32 s · 15 · 13 · 7 · Universal set & Venn compl…

12 questions · Seed 51 · 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 47 students, n(A) = 18, n(B) = 19, and n(A ∩ B) = 7. How many students are in neither A nor B?
17
By inclusion-exclusion, n(A ∪ B) = 18 + 19 − 7 = 30, leaving 47 − 30 = 17 in neither set.
2. In a group of 44 students, n(A) = 17, n(B) = 24, and n(A ∩ B) = 8. How many students are in neither A nor B?
11
By inclusion-exclusion, n(A ∪ B) = 17 + 24 − 8 = 33, leaving 44 − 33 = 11 in neither set.
3. In a group of 60 students, n(A) = 23, n(B) = 28, and n(A ∩ B) = 9. How many students are in neither A nor B?
18
By inclusion-exclusion, n(A ∪ B) = 23 + 28 − 9 = 42, leaving 60 − 42 = 18 in neither set.
4. In a group of 39 students, n(A) = 12, n(B) = 16, and n(A ∩ B) = 7. How many students are in neither A nor B?
18
By inclusion-exclusion, n(A ∪ B) = 12 + 16 − 7 = 21, leaving 39 − 21 = 18 in neither set.
5. In a group of 33 students, n(A) = 11, n(B) = 15, and n(A ∩ B) = 7. How many students are in neither A nor B?
14
By inclusion-exclusion, n(A ∪ B) = 11 + 15 − 7 = 19, leaving 33 − 19 = 14 in neither set.
6. In a group of 28 students, n(A) = 11, n(B) = 14, and n(A ∩ B) = 5. How many students are in neither A nor B?
8
By inclusion-exclusion, n(A ∪ B) = 11 + 14 − 5 = 20, leaving 28 − 20 = 8 in neither set.
7. In a group of 28 students, n(A) = 20, n(B) = 11, and n(A ∩ B) = 6. How many students are in neither A nor B?
3
By inclusion-exclusion, n(A ∪ B) = 20 + 11 − 6 = 25, leaving 28 − 25 = 3 in neither set.
8. In a group of 43 students, n(A) = 20, n(B) = 19, and n(A ∩ B) = 11. How many students are in neither A nor B?
15
By inclusion-exclusion, n(A ∪ B) = 20 + 19 − 11 = 28, leaving 43 − 28 = 15 in neither set.
9. In a group of 38 students, n(A) = 12, n(B) = 25, and n(A ∩ B) = 7. How many students are in neither A nor B?
8
By inclusion-exclusion, n(A ∪ B) = 12 + 25 − 7 = 30, leaving 38 − 30 = 8 in neither set.
10. In a group of 57 students, n(A) = 20, n(B) = 28, and n(A ∩ B) = 9. How many students are in neither A nor B?
18
By inclusion-exclusion, n(A ∪ B) = 20 + 28 − 9 = 39, leaving 57 − 39 = 18 in neither set.
11. In a group of 51 students, n(A) = 15, n(B) = 29, and n(A ∩ B) = 10. How many students are in neither A nor B?
17
By inclusion-exclusion, n(A ∪ B) = 15 + 29 − 10 = 34, leaving 51 − 34 = 17 in neither set.
12. In a group of 32 students, n(A) = 15, n(B) = 13, and n(A ∩ B) = 7. How many students are in neither A nor B?
11
By inclusion-exclusion, n(A ∪ B) = 15 + 13 − 7 = 21, leaving 32 − 21 = 11 in neither set.

12 questions · Seed 51 · 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 47 students, n(A) = 18, n(B) = 19, and n(A ∩ B) = 7. How many students are in neither A nor B?
47 s · 18 · 19 · 7 · Universal set & Venn compl…
2. In a group of 44 students, n(A) = 17, n(B) = 24, and n(A ∩ B) = 8. How many students are in neither A nor B?
44 s · 17 · 24 · 8 · Universal set & Venn compl…
3. In a group of 60 students, n(A) = 23, n(B) = 28, and n(A ∩ B) = 9. How many students are in neither A nor B?
60 s · 23 · 28 · 9 · Universal set & Venn compl…
4. In a group of 39 students, n(A) = 12, n(B) = 16, and n(A ∩ B) = 7. How many students are in neither A nor B?
39 s · 12 · 16 · 7 · Universal set & Venn compl…
5. In a group of 33 students, n(A) = 11, n(B) = 15, and n(A ∩ B) = 7. How many students are in neither A nor B?
33 s · 11 · 15 · 7 · Universal set & Venn compl…
6. In a group of 28 students, n(A) = 11, n(B) = 14, and n(A ∩ B) = 5. How many students are in neither A nor B?
28 s · 11 · 14 · 5 · Universal set & Venn compl…
7. In a group of 28 students, n(A) = 20, n(B) = 11, and n(A ∩ B) = 6. How many students are in neither A nor B?
28 s · 20 · 11 · 6 · Universal set & Venn compl…
8. In a group of 43 students, n(A) = 20, n(B) = 19, and n(A ∩ B) = 11. How many students are in neither A nor B?
43 s · 20 · 19 · 11 · Universal set & Venn compl…
9. In a group of 38 students, n(A) = 12, n(B) = 25, and n(A ∩ B) = 7. How many students are in neither A nor B?
38 s · 12 · 25 · 7 · Universal set & Venn compl…
10. In a group of 57 students, n(A) = 20, n(B) = 28, and n(A ∩ B) = 9. How many students are in neither A nor B?
57 s · 20 · 28 · 9 · Universal set & Venn compl…
11. In a group of 51 students, n(A) = 15, n(B) = 29, and n(A ∩ B) = 10. How many students are in neither A nor B?
51 s · 15 · 29 · 10 · Universal set & Venn compl…
12. In a group of 32 students, n(A) = 15, n(B) = 13, and n(A ∩ B) = 7. How many students are in neither A nor B?
32 s · 15 · 13 · 7 · Universal set & Venn compl…

12 questions · Seed 51 · 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 47 students, n(A) = 18, n(B) = 19, and n(A ∩ B) = 7. How many students are in neither A nor B?
17
By inclusion-exclusion, n(A ∪ B) = 18 + 19 − 7 = 30, leaving 47 − 30 = 17 in neither set.
2. In a group of 44 students, n(A) = 17, n(B) = 24, and n(A ∩ B) = 8. How many students are in neither A nor B?
11
By inclusion-exclusion, n(A ∪ B) = 17 + 24 − 8 = 33, leaving 44 − 33 = 11 in neither set.
3. In a group of 60 students, n(A) = 23, n(B) = 28, and n(A ∩ B) = 9. How many students are in neither A nor B?
18
By inclusion-exclusion, n(A ∪ B) = 23 + 28 − 9 = 42, leaving 60 − 42 = 18 in neither set.
4. In a group of 39 students, n(A) = 12, n(B) = 16, and n(A ∩ B) = 7. How many students are in neither A nor B?
18
By inclusion-exclusion, n(A ∪ B) = 12 + 16 − 7 = 21, leaving 39 − 21 = 18 in neither set.
5. In a group of 33 students, n(A) = 11, n(B) = 15, and n(A ∩ B) = 7. How many students are in neither A nor B?
14
By inclusion-exclusion, n(A ∪ B) = 11 + 15 − 7 = 19, leaving 33 − 19 = 14 in neither set.
6. In a group of 28 students, n(A) = 11, n(B) = 14, and n(A ∩ B) = 5. How many students are in neither A nor B?
8
By inclusion-exclusion, n(A ∪ B) = 11 + 14 − 5 = 20, leaving 28 − 20 = 8 in neither set.
7. In a group of 28 students, n(A) = 20, n(B) = 11, and n(A ∩ B) = 6. How many students are in neither A nor B?
3
By inclusion-exclusion, n(A ∪ B) = 20 + 11 − 6 = 25, leaving 28 − 25 = 3 in neither set.
8. In a group of 43 students, n(A) = 20, n(B) = 19, and n(A ∩ B) = 11. How many students are in neither A nor B?
15
By inclusion-exclusion, n(A ∪ B) = 20 + 19 − 11 = 28, leaving 43 − 28 = 15 in neither set.
9. In a group of 38 students, n(A) = 12, n(B) = 25, and n(A ∩ B) = 7. How many students are in neither A nor B?
8
By inclusion-exclusion, n(A ∪ B) = 12 + 25 − 7 = 30, leaving 38 − 30 = 8 in neither set.
10. In a group of 57 students, n(A) = 20, n(B) = 28, and n(A ∩ B) = 9. How many students are in neither A nor B?
18
By inclusion-exclusion, n(A ∪ B) = 20 + 28 − 9 = 39, leaving 57 − 39 = 18 in neither set.
11. In a group of 51 students, n(A) = 15, n(B) = 29, and n(A ∩ B) = 10. How many students are in neither A nor B?
17
By inclusion-exclusion, n(A ∪ B) = 15 + 29 − 10 = 34, leaving 51 − 34 = 17 in neither set.
12. In a group of 32 students, n(A) = 15, n(B) = 13, and n(A ∩ B) = 7. How many students are in neither A nor B?
11
By inclusion-exclusion, n(A ∪ B) = 15 + 13 − 7 = 21, leaving 32 − 21 = 11 in neither set.

12 questions · Seed 51 · Age guidance, not curriculum certification