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 39 students, n(A) = 16, n(B) = 13, and n(A ∩ B) = 5. How many students are in neither A nor B?
39 s · 16 · 13 · 5 · Universal set & Venn compl…
2. In a group of 40 students, n(A) = 18, n(B) = 11, and n(A ∩ B) = 6. How many students are in neither A nor B?
40 s · 18 · 11 · 6 · Universal set & Venn compl…
3. In a group of 29 students, n(A) = 13, n(B) = 14, and n(A ∩ B) = 6. How many students are in neither A nor B?
29 s · 13 · 14 · 6 · Universal set & Venn compl…
4. In a group of 51 students, n(A) = 27, n(B) = 29, and n(A ∩ B) = 11. How many students are in neither A nor B?
51 s · 27 · 29 · 11 · Universal set & Venn compl…
5. In a group of 55 students, n(A) = 26, n(B) = 23, and n(A ∩ B) = 6. How many students are in neither A nor B?
55 s · 26 · 23 · 6 · Universal set & Venn compl…
6. In a group of 40 students, n(A) = 21, n(B) = 11, and n(A ∩ B) = 5. How many students are in neither A nor B?
40 s · 21 · 11 · 5 · Universal set & Venn compl…
7. In a group of 34 students, n(A) = 15, n(B) = 23, and n(A ∩ B) = 11. How many students are in neither A nor B?
34 s · 15 · 23 · 11 · Universal set & Venn compl…
8. In a group of 53 students, n(A) = 30, n(B) = 30, and n(A ∩ B) = 10. How many students are in neither A nor B?
53 s · 30 · 30 · 10 · Universal set & Venn compl…
9. In a group of 29 students, n(A) = 18, n(B) = 14, and n(A ∩ B) = 8. How many students are in neither A nor B?
29 s · 18 · 14 · 8 · Universal set & Venn compl…
10. In a group of 50 students, n(A) = 29, n(B) = 22, and n(A ∩ B) = 12. How many students are in neither A nor B?
50 s · 29 · 22 · 12 · Universal set & Venn compl…
11. In a group of 42 students, n(A) = 21, n(B) = 23, and n(A ∩ B) = 11. How many students are in neither A nor B?
42 s · 21 · 23 · 11 · Universal set & Venn compl…
12. In a group of 41 students, n(A) = 14, n(B) = 23, and n(A ∩ B) = 10. How many students are in neither A nor B?
41 s · 14 · 23 · 10 · Universal set & Venn compl…

12 questions · Seed 47 · 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 39 students, n(A) = 16, n(B) = 13, and n(A ∩ B) = 5. How many students are in neither A nor B?
15
By inclusion-exclusion, n(A ∪ B) = 16 + 13 − 5 = 24, leaving 39 − 24 = 15 in neither set.
2. In a group of 40 students, n(A) = 18, n(B) = 11, and n(A ∩ B) = 6. How many students are in neither A nor B?
17
By inclusion-exclusion, n(A ∪ B) = 18 + 11 − 6 = 23, leaving 40 − 23 = 17 in neither set.
3. In a group of 29 students, n(A) = 13, n(B) = 14, and n(A ∩ B) = 6. How many students are in neither A nor B?
8
By inclusion-exclusion, n(A ∪ B) = 13 + 14 − 6 = 21, leaving 29 − 21 = 8 in neither set.
4. In a group of 51 students, n(A) = 27, n(B) = 29, and n(A ∩ B) = 11. How many students are in neither A nor B?
6
By inclusion-exclusion, n(A ∪ B) = 27 + 29 − 11 = 45, leaving 51 − 45 = 6 in neither set.
5. In a group of 55 students, n(A) = 26, n(B) = 23, and n(A ∩ B) = 6. How many students are in neither A nor B?
12
By inclusion-exclusion, n(A ∪ B) = 26 + 23 − 6 = 43, leaving 55 − 43 = 12 in neither set.
6. In a group of 40 students, n(A) = 21, n(B) = 11, and n(A ∩ B) = 5. How many students are in neither A nor B?
13
By inclusion-exclusion, n(A ∪ B) = 21 + 11 − 5 = 27, leaving 40 − 27 = 13 in neither set.
7. In a group of 34 students, n(A) = 15, n(B) = 23, and n(A ∩ B) = 11. How many students are in neither A nor B?
7
By inclusion-exclusion, n(A ∪ B) = 15 + 23 − 11 = 27, leaving 34 − 27 = 7 in neither set.
8. In a group of 53 students, n(A) = 30, n(B) = 30, and n(A ∩ B) = 10. How many students are in neither A nor B?
3
By inclusion-exclusion, n(A ∪ B) = 30 + 30 − 10 = 50, leaving 53 − 50 = 3 in neither set.
9. In a group of 29 students, n(A) = 18, n(B) = 14, and n(A ∩ B) = 8. How many students are in neither A nor B?
5
By inclusion-exclusion, n(A ∪ B) = 18 + 14 − 8 = 24, leaving 29 − 24 = 5 in neither set.
10. In a group of 50 students, n(A) = 29, n(B) = 22, and n(A ∩ B) = 12. How many students are in neither A nor B?
11
By inclusion-exclusion, n(A ∪ B) = 29 + 22 − 12 = 39, leaving 50 − 39 = 11 in neither set.
11. In a group of 42 students, n(A) = 21, n(B) = 23, and n(A ∩ B) = 11. How many students are in neither A nor B?
9
By inclusion-exclusion, n(A ∪ B) = 21 + 23 − 11 = 33, leaving 42 − 33 = 9 in neither set.
12. In a group of 41 students, n(A) = 14, n(B) = 23, and n(A ∩ B) = 10. How many students are in neither A nor B?
14
By inclusion-exclusion, n(A ∪ B) = 14 + 23 − 10 = 27, leaving 41 − 27 = 14 in neither set.

12 questions · Seed 47 · 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 39 students, n(A) = 16, n(B) = 13, and n(A ∩ B) = 5. How many students are in neither A nor B?
39 s · 16 · 13 · 5 · Universal set & Venn compl…
2. In a group of 40 students, n(A) = 18, n(B) = 11, and n(A ∩ B) = 6. How many students are in neither A nor B?
40 s · 18 · 11 · 6 · Universal set & Venn compl…
3. In a group of 29 students, n(A) = 13, n(B) = 14, and n(A ∩ B) = 6. How many students are in neither A nor B?
29 s · 13 · 14 · 6 · Universal set & Venn compl…
4. In a group of 51 students, n(A) = 27, n(B) = 29, and n(A ∩ B) = 11. How many students are in neither A nor B?
51 s · 27 · 29 · 11 · Universal set & Venn compl…
5. In a group of 55 students, n(A) = 26, n(B) = 23, and n(A ∩ B) = 6. How many students are in neither A nor B?
55 s · 26 · 23 · 6 · Universal set & Venn compl…
6. In a group of 40 students, n(A) = 21, n(B) = 11, and n(A ∩ B) = 5. How many students are in neither A nor B?
40 s · 21 · 11 · 5 · Universal set & Venn compl…
7. In a group of 34 students, n(A) = 15, n(B) = 23, and n(A ∩ B) = 11. How many students are in neither A nor B?
34 s · 15 · 23 · 11 · Universal set & Venn compl…
8. In a group of 53 students, n(A) = 30, n(B) = 30, and n(A ∩ B) = 10. How many students are in neither A nor B?
53 s · 30 · 30 · 10 · Universal set & Venn compl…
9. In a group of 29 students, n(A) = 18, n(B) = 14, and n(A ∩ B) = 8. How many students are in neither A nor B?
29 s · 18 · 14 · 8 · Universal set & Venn compl…
10. In a group of 50 students, n(A) = 29, n(B) = 22, and n(A ∩ B) = 12. How many students are in neither A nor B?
50 s · 29 · 22 · 12 · Universal set & Venn compl…
11. In a group of 42 students, n(A) = 21, n(B) = 23, and n(A ∩ B) = 11. How many students are in neither A nor B?
42 s · 21 · 23 · 11 · Universal set & Venn compl…
12. In a group of 41 students, n(A) = 14, n(B) = 23, and n(A ∩ B) = 10. How many students are in neither A nor B?
41 s · 14 · 23 · 10 · Universal set & Venn compl…

12 questions · Seed 47 · 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 39 students, n(A) = 16, n(B) = 13, and n(A ∩ B) = 5. How many students are in neither A nor B?
15
By inclusion-exclusion, n(A ∪ B) = 16 + 13 − 5 = 24, leaving 39 − 24 = 15 in neither set.
2. In a group of 40 students, n(A) = 18, n(B) = 11, and n(A ∩ B) = 6. How many students are in neither A nor B?
17
By inclusion-exclusion, n(A ∪ B) = 18 + 11 − 6 = 23, leaving 40 − 23 = 17 in neither set.
3. In a group of 29 students, n(A) = 13, n(B) = 14, and n(A ∩ B) = 6. How many students are in neither A nor B?
8
By inclusion-exclusion, n(A ∪ B) = 13 + 14 − 6 = 21, leaving 29 − 21 = 8 in neither set.
4. In a group of 51 students, n(A) = 27, n(B) = 29, and n(A ∩ B) = 11. How many students are in neither A nor B?
6
By inclusion-exclusion, n(A ∪ B) = 27 + 29 − 11 = 45, leaving 51 − 45 = 6 in neither set.
5. In a group of 55 students, n(A) = 26, n(B) = 23, and n(A ∩ B) = 6. How many students are in neither A nor B?
12
By inclusion-exclusion, n(A ∪ B) = 26 + 23 − 6 = 43, leaving 55 − 43 = 12 in neither set.
6. In a group of 40 students, n(A) = 21, n(B) = 11, and n(A ∩ B) = 5. How many students are in neither A nor B?
13
By inclusion-exclusion, n(A ∪ B) = 21 + 11 − 5 = 27, leaving 40 − 27 = 13 in neither set.
7. In a group of 34 students, n(A) = 15, n(B) = 23, and n(A ∩ B) = 11. How many students are in neither A nor B?
7
By inclusion-exclusion, n(A ∪ B) = 15 + 23 − 11 = 27, leaving 34 − 27 = 7 in neither set.
8. In a group of 53 students, n(A) = 30, n(B) = 30, and n(A ∩ B) = 10. How many students are in neither A nor B?
3
By inclusion-exclusion, n(A ∪ B) = 30 + 30 − 10 = 50, leaving 53 − 50 = 3 in neither set.
9. In a group of 29 students, n(A) = 18, n(B) = 14, and n(A ∩ B) = 8. How many students are in neither A nor B?
5
By inclusion-exclusion, n(A ∪ B) = 18 + 14 − 8 = 24, leaving 29 − 24 = 5 in neither set.
10. In a group of 50 students, n(A) = 29, n(B) = 22, and n(A ∩ B) = 12. How many students are in neither A nor B?
11
By inclusion-exclusion, n(A ∪ B) = 29 + 22 − 12 = 39, leaving 50 − 39 = 11 in neither set.
11. In a group of 42 students, n(A) = 21, n(B) = 23, and n(A ∩ B) = 11. How many students are in neither A nor B?
9
By inclusion-exclusion, n(A ∪ B) = 21 + 23 − 11 = 33, leaving 42 − 33 = 9 in neither set.
12. In a group of 41 students, n(A) = 14, n(B) = 23, and n(A ∩ B) = 10. How many students are in neither A nor B?
14
By inclusion-exclusion, n(A ∪ B) = 14 + 23 − 10 = 27, leaving 41 − 27 = 14 in neither set.

12 questions · Seed 47 · Age guidance, not curriculum certification