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 39 students, n(A) = 28, n(B) = 16, and n(A ∩ B) = 10. How many students are in neither A nor B?
39 s · 28 · 16 · 10 · Universal set & Venn compl…
2. In a group of 39 students, n(A) = 25, n(B) = 22, and n(A ∩ B) = 11. How many students are in neither A nor B?
39 s · 25 · 22 · 11 · Universal set & Venn compl…
3. In a group of 47 students, n(A) = 26, n(B) = 28, and n(A ∩ B) = 10. How many students are in neither A nor B?
47 s · 26 · 28 · 10 · Universal set & Venn compl…
4. In a group of 37 students, n(A) = 29, n(B) = 16, and n(A ∩ B) = 11. How many students are in neither A nor B?
37 s · 29 · 16 · 11 · Universal set & Venn compl…
5. In a group of 36 students, n(A) = 11, n(B) = 15, and n(A ∩ B) = 2. How many students are in neither A nor B?
36 s · 11 · 15 · 2 · Universal set & Venn compl…
6. In a group of 28 students, n(A) = 12, n(B) = 16, and n(A ∩ B) = 7. How many students are in neither A nor B?
28 s · 12 · 16 · 7 · Universal set & Venn compl…
7. In a group of 44 students, n(A) = 25, n(B) = 25, and n(A ∩ B) = 11. How many students are in neither A nor B?
44 s · 25 · 25 · 11 · Universal set & Venn compl…
8. In a group of 38 students, n(A) = 21, n(B) = 25, and n(A ∩ B) = 11. How many students are in neither A nor B?
38 s · 21 · 25 · 11 · Universal set & Venn compl…
9. In a group of 46 students, n(A) = 27, n(B) = 16, and n(A ∩ B) = 9. How many students are in neither A nor B?
46 s · 27 · 16 · 9 · Universal set & Venn compl…
10. In a group of 40 students, n(A) = 17, n(B) = 22, and n(A ∩ B) = 9. How many students are in neither A nor B?
40 s · 17 · 22 · 9 · Universal set & Venn compl…
11. In a group of 46 students, n(A) = 20, n(B) = 17, and n(A ∩ B) = 8. How many students are in neither A nor B?
46 s · 20 · 17 · 8 · Universal set & Venn compl…
12. In a group of 36 students, n(A) = 17, n(B) = 10, and n(A ∩ B) = 3. How many students are in neither A nor B?
36 s · 17 · 10 · 3 · Universal set & Venn compl…

12 questions · Seed 104736 · 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 39 students, n(A) = 28, n(B) = 16, and n(A ∩ B) = 10. How many students are in neither A nor B?
5
By inclusion-exclusion, n(A ∪ B) = 28 + 16 − 10 = 34, leaving 39 − 34 = 5 in neither set.
2. In a group of 39 students, n(A) = 25, n(B) = 22, and n(A ∩ B) = 11. How many students are in neither A nor B?
3
By inclusion-exclusion, n(A ∪ B) = 25 + 22 − 11 = 36, leaving 39 − 36 = 3 in neither set.
3. In a group of 47 students, n(A) = 26, n(B) = 28, and n(A ∩ B) = 10. How many students are in neither A nor B?
3
By inclusion-exclusion, n(A ∪ B) = 26 + 28 − 10 = 44, leaving 47 − 44 = 3 in neither set.
4. In a group of 37 students, n(A) = 29, n(B) = 16, and n(A ∩ B) = 11. How many students are in neither A nor B?
3
By inclusion-exclusion, n(A ∪ B) = 29 + 16 − 11 = 34, leaving 37 − 34 = 3 in neither set.
5. In a group of 36 students, n(A) = 11, n(B) = 15, and n(A ∩ B) = 2. How many students are in neither A nor B?
12
By inclusion-exclusion, n(A ∪ B) = 11 + 15 − 2 = 24, leaving 36 − 24 = 12 in neither set.
6. In a group of 28 students, n(A) = 12, n(B) = 16, and n(A ∩ B) = 7. How many students are in neither A nor B?
7
By inclusion-exclusion, n(A ∪ B) = 12 + 16 − 7 = 21, leaving 28 − 21 = 7 in neither set.
7. In a group of 44 students, n(A) = 25, n(B) = 25, and n(A ∩ B) = 11. How many students are in neither A nor B?
5
By inclusion-exclusion, n(A ∪ B) = 25 + 25 − 11 = 39, leaving 44 − 39 = 5 in neither set.
8. In a group of 38 students, n(A) = 21, n(B) = 25, and n(A ∩ B) = 11. How many students are in neither A nor B?
3
By inclusion-exclusion, n(A ∪ B) = 21 + 25 − 11 = 35, leaving 38 − 35 = 3 in neither set.
9. In a group of 46 students, n(A) = 27, n(B) = 16, and n(A ∩ B) = 9. How many students are in neither A nor B?
12
By inclusion-exclusion, n(A ∪ B) = 27 + 16 − 9 = 34, leaving 46 − 34 = 12 in neither set.
10. In a group of 40 students, n(A) = 17, n(B) = 22, and n(A ∩ B) = 9. How many students are in neither A nor B?
10
By inclusion-exclusion, n(A ∪ B) = 17 + 22 − 9 = 30, leaving 40 − 30 = 10 in neither set.
11. In a group of 46 students, n(A) = 20, n(B) = 17, and n(A ∩ B) = 8. How many students are in neither A nor B?
17
By inclusion-exclusion, n(A ∪ B) = 20 + 17 − 8 = 29, leaving 46 − 29 = 17 in neither set.
12. In a group of 36 students, n(A) = 17, n(B) = 10, and n(A ∩ B) = 3. How many students are in neither A nor B?
12
By inclusion-exclusion, n(A ∪ B) = 17 + 10 − 3 = 24, leaving 36 − 24 = 12 in neither set.

12 questions · Seed 104736 · 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 39 students, n(A) = 28, n(B) = 16, and n(A ∩ B) = 10. How many students are in neither A nor B?
39 s · 28 · 16 · 10 · Universal set & Venn compl…
2. In a group of 39 students, n(A) = 25, n(B) = 22, and n(A ∩ B) = 11. How many students are in neither A nor B?
39 s · 25 · 22 · 11 · Universal set & Venn compl…
3. In a group of 47 students, n(A) = 26, n(B) = 28, and n(A ∩ B) = 10. How many students are in neither A nor B?
47 s · 26 · 28 · 10 · Universal set & Venn compl…
4. In a group of 37 students, n(A) = 29, n(B) = 16, and n(A ∩ B) = 11. How many students are in neither A nor B?
37 s · 29 · 16 · 11 · Universal set & Venn compl…
5. In a group of 36 students, n(A) = 11, n(B) = 15, and n(A ∩ B) = 2. How many students are in neither A nor B?
36 s · 11 · 15 · 2 · Universal set & Venn compl…
6. In a group of 28 students, n(A) = 12, n(B) = 16, and n(A ∩ B) = 7. How many students are in neither A nor B?
28 s · 12 · 16 · 7 · Universal set & Venn compl…
7. In a group of 44 students, n(A) = 25, n(B) = 25, and n(A ∩ B) = 11. How many students are in neither A nor B?
44 s · 25 · 25 · 11 · Universal set & Venn compl…
8. In a group of 38 students, n(A) = 21, n(B) = 25, and n(A ∩ B) = 11. How many students are in neither A nor B?
38 s · 21 · 25 · 11 · Universal set & Venn compl…
9. In a group of 46 students, n(A) = 27, n(B) = 16, and n(A ∩ B) = 9. How many students are in neither A nor B?
46 s · 27 · 16 · 9 · Universal set & Venn compl…
10. In a group of 40 students, n(A) = 17, n(B) = 22, and n(A ∩ B) = 9. How many students are in neither A nor B?
40 s · 17 · 22 · 9 · Universal set & Venn compl…
11. In a group of 46 students, n(A) = 20, n(B) = 17, and n(A ∩ B) = 8. How many students are in neither A nor B?
46 s · 20 · 17 · 8 · Universal set & Venn compl…
12. In a group of 36 students, n(A) = 17, n(B) = 10, and n(A ∩ B) = 3. How many students are in neither A nor B?
36 s · 17 · 10 · 3 · Universal set & Venn compl…

12 questions · Seed 104736 · 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 39 students, n(A) = 28, n(B) = 16, and n(A ∩ B) = 10. How many students are in neither A nor B?
5
By inclusion-exclusion, n(A ∪ B) = 28 + 16 − 10 = 34, leaving 39 − 34 = 5 in neither set.
2. In a group of 39 students, n(A) = 25, n(B) = 22, and n(A ∩ B) = 11. How many students are in neither A nor B?
3
By inclusion-exclusion, n(A ∪ B) = 25 + 22 − 11 = 36, leaving 39 − 36 = 3 in neither set.
3. In a group of 47 students, n(A) = 26, n(B) = 28, and n(A ∩ B) = 10. How many students are in neither A nor B?
3
By inclusion-exclusion, n(A ∪ B) = 26 + 28 − 10 = 44, leaving 47 − 44 = 3 in neither set.
4. In a group of 37 students, n(A) = 29, n(B) = 16, and n(A ∩ B) = 11. How many students are in neither A nor B?
3
By inclusion-exclusion, n(A ∪ B) = 29 + 16 − 11 = 34, leaving 37 − 34 = 3 in neither set.
5. In a group of 36 students, n(A) = 11, n(B) = 15, and n(A ∩ B) = 2. How many students are in neither A nor B?
12
By inclusion-exclusion, n(A ∪ B) = 11 + 15 − 2 = 24, leaving 36 − 24 = 12 in neither set.
6. In a group of 28 students, n(A) = 12, n(B) = 16, and n(A ∩ B) = 7. How many students are in neither A nor B?
7
By inclusion-exclusion, n(A ∪ B) = 12 + 16 − 7 = 21, leaving 28 − 21 = 7 in neither set.
7. In a group of 44 students, n(A) = 25, n(B) = 25, and n(A ∩ B) = 11. How many students are in neither A nor B?
5
By inclusion-exclusion, n(A ∪ B) = 25 + 25 − 11 = 39, leaving 44 − 39 = 5 in neither set.
8. In a group of 38 students, n(A) = 21, n(B) = 25, and n(A ∩ B) = 11. How many students are in neither A nor B?
3
By inclusion-exclusion, n(A ∪ B) = 21 + 25 − 11 = 35, leaving 38 − 35 = 3 in neither set.
9. In a group of 46 students, n(A) = 27, n(B) = 16, and n(A ∩ B) = 9. How many students are in neither A nor B?
12
By inclusion-exclusion, n(A ∪ B) = 27 + 16 − 9 = 34, leaving 46 − 34 = 12 in neither set.
10. In a group of 40 students, n(A) = 17, n(B) = 22, and n(A ∩ B) = 9. How many students are in neither A nor B?
10
By inclusion-exclusion, n(A ∪ B) = 17 + 22 − 9 = 30, leaving 40 − 30 = 10 in neither set.
11. In a group of 46 students, n(A) = 20, n(B) = 17, and n(A ∩ B) = 8. How many students are in neither A nor B?
17
By inclusion-exclusion, n(A ∪ B) = 20 + 17 − 8 = 29, leaving 46 − 29 = 17 in neither set.
12. In a group of 36 students, n(A) = 17, n(B) = 10, and n(A ∩ B) = 3. How many students are in neither A nor B?
12
By inclusion-exclusion, n(A ∪ B) = 17 + 10 − 3 = 24, leaving 36 − 24 = 12 in neither set.

12 questions · Seed 104736 · Age guidance, not curriculum certification