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 38 students, n(A) = 24, n(B) = 17, and n(A ∩ B) = 11. How many students are in neither A nor B?
38 s · 24 · 17 · 11 · Universal set & Venn compl…
2. In a group of 29 students, n(A) = 9, n(B) = 14, and n(A ∩ B) = 4. How many students are in neither A nor B?
29 s · 9 · 14 · 4 · Universal set & Venn compl…
3. In a group of 38 students, n(A) = 12, n(B) = 17, and n(A ∩ B) = 2. How many students are in neither A nor B?
38 s · 12 · 17 · 2 · Universal set & Venn compl…
4. In a group of 38 students, n(A) = 16, n(B) = 15, and n(A ∩ B) = 4. How many students are in neither A nor B?
38 s · 16 · 15 · 4 · Universal set & Venn compl…
5. In a group of 50 students, n(A) = 23, n(B) = 27, and n(A ∩ B) = 8. How many students are in neither A nor B?
50 s · 23 · 27 · 8 · Universal set & Venn compl…
6. In a group of 30 students, n(A) = 15, n(B) = 7, and n(A ∩ B) = 3. How many students are in neither A nor B?
30 s · 15 · 7 · 3 · Universal set & Venn compl…
7. In a group of 39 students, n(A) = 15, n(B) = 25, and n(A ∩ B) = 7. How many students are in neither A nor B?
39 s · 15 · 25 · 7 · Universal set & Venn compl…
8. In a group of 33 students, n(A) = 20, n(B) = 11, and n(A ∩ B) = 3. How many students are in neither A nor B?
33 s · 20 · 11 · 3 · Universal set & Venn compl…
9. In a group of 39 students, n(A) = 24, n(B) = 11, and n(A ∩ B) = 4. How many students are in neither A nor B?
39 s · 24 · 11 · 4 · Universal set & Venn compl…
10. In a group of 44 students, n(A) = 20, n(B) = 25, and n(A ∩ B) = 11. How many students are in neither A nor B?
44 s · 20 · 25 · 11 · Universal set & Venn compl…
11. In a group of 50 students, n(A) = 24, n(B) = 31, and n(A ∩ B) = 11. How many students are in neither A nor B?
50 s · 24 · 31 · 11 · Universal set & Venn compl…
12. In a group of 33 students, n(A) = 10, n(B) = 9, and n(A ∩ B) = 2. How many students are in neither A nor B?
33 s · 10 · 9 · 2 · Universal set & Venn compl…

12 questions · Seed 42 · 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 38 students, n(A) = 24, n(B) = 17, and n(A ∩ B) = 11. How many students are in neither A nor B?
8
By inclusion-exclusion, n(A ∪ B) = 24 + 17 − 11 = 30, leaving 38 − 30 = 8 in neither set.
2. In a group of 29 students, n(A) = 9, n(B) = 14, and n(A ∩ B) = 4. How many students are in neither A nor B?
10
By inclusion-exclusion, n(A ∪ B) = 9 + 14 − 4 = 19, leaving 29 − 19 = 10 in neither set.
3. In a group of 38 students, n(A) = 12, n(B) = 17, and n(A ∩ B) = 2. How many students are in neither A nor B?
11
By inclusion-exclusion, n(A ∪ B) = 12 + 17 − 2 = 27, leaving 38 − 27 = 11 in neither set.
4. In a group of 38 students, n(A) = 16, n(B) = 15, and n(A ∩ B) = 4. How many students are in neither A nor B?
11
By inclusion-exclusion, n(A ∪ B) = 16 + 15 − 4 = 27, leaving 38 − 27 = 11 in neither set.
5. In a group of 50 students, n(A) = 23, n(B) = 27, and n(A ∩ B) = 8. How many students are in neither A nor B?
8
By inclusion-exclusion, n(A ∪ B) = 23 + 27 − 8 = 42, leaving 50 − 42 = 8 in neither set.
6. In a group of 30 students, n(A) = 15, n(B) = 7, and n(A ∩ B) = 3. How many students are in neither A nor B?
11
By inclusion-exclusion, n(A ∪ B) = 15 + 7 − 3 = 19, leaving 30 − 19 = 11 in neither set.
7. In a group of 39 students, n(A) = 15, n(B) = 25, and n(A ∩ B) = 7. How many students are in neither A nor B?
6
By inclusion-exclusion, n(A ∪ B) = 15 + 25 − 7 = 33, leaving 39 − 33 = 6 in neither set.
8. In a group of 33 students, n(A) = 20, n(B) = 11, and n(A ∩ B) = 3. How many students are in neither A nor B?
5
By inclusion-exclusion, n(A ∪ B) = 20 + 11 − 3 = 28, leaving 33 − 28 = 5 in neither set.
9. In a group of 39 students, n(A) = 24, n(B) = 11, and n(A ∩ B) = 4. How many students are in neither A nor B?
8
By inclusion-exclusion, n(A ∪ B) = 24 + 11 − 4 = 31, leaving 39 − 31 = 8 in neither set.
10. In a group of 44 students, n(A) = 20, n(B) = 25, and n(A ∩ B) = 11. How many students are in neither A nor B?
10
By inclusion-exclusion, n(A ∪ B) = 20 + 25 − 11 = 34, leaving 44 − 34 = 10 in neither set.
11. In a group of 50 students, n(A) = 24, n(B) = 31, and n(A ∩ B) = 11. How many students are in neither A nor B?
6
By inclusion-exclusion, n(A ∪ B) = 24 + 31 − 11 = 44, leaving 50 − 44 = 6 in neither set.
12. In a group of 33 students, n(A) = 10, n(B) = 9, and n(A ∩ B) = 2. How many students are in neither A nor B?
16
By inclusion-exclusion, n(A ∪ B) = 10 + 9 − 2 = 17, leaving 33 − 17 = 16 in neither set.

12 questions · Seed 42 · 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 38 students, n(A) = 24, n(B) = 17, and n(A ∩ B) = 11. How many students are in neither A nor B?
38 s · 24 · 17 · 11 · Universal set & Venn compl…
2. In a group of 29 students, n(A) = 9, n(B) = 14, and n(A ∩ B) = 4. How many students are in neither A nor B?
29 s · 9 · 14 · 4 · Universal set & Venn compl…
3. In a group of 38 students, n(A) = 12, n(B) = 17, and n(A ∩ B) = 2. How many students are in neither A nor B?
38 s · 12 · 17 · 2 · Universal set & Venn compl…
4. In a group of 38 students, n(A) = 16, n(B) = 15, and n(A ∩ B) = 4. How many students are in neither A nor B?
38 s · 16 · 15 · 4 · Universal set & Venn compl…
5. In a group of 50 students, n(A) = 23, n(B) = 27, and n(A ∩ B) = 8. How many students are in neither A nor B?
50 s · 23 · 27 · 8 · Universal set & Venn compl…
6. In a group of 30 students, n(A) = 15, n(B) = 7, and n(A ∩ B) = 3. How many students are in neither A nor B?
30 s · 15 · 7 · 3 · Universal set & Venn compl…
7. In a group of 39 students, n(A) = 15, n(B) = 25, and n(A ∩ B) = 7. How many students are in neither A nor B?
39 s · 15 · 25 · 7 · Universal set & Venn compl…
8. In a group of 33 students, n(A) = 20, n(B) = 11, and n(A ∩ B) = 3. How many students are in neither A nor B?
33 s · 20 · 11 · 3 · Universal set & Venn compl…
9. In a group of 39 students, n(A) = 24, n(B) = 11, and n(A ∩ B) = 4. How many students are in neither A nor B?
39 s · 24 · 11 · 4 · Universal set & Venn compl…
10. In a group of 44 students, n(A) = 20, n(B) = 25, and n(A ∩ B) = 11. How many students are in neither A nor B?
44 s · 20 · 25 · 11 · Universal set & Venn compl…
11. In a group of 50 students, n(A) = 24, n(B) = 31, and n(A ∩ B) = 11. How many students are in neither A nor B?
50 s · 24 · 31 · 11 · Universal set & Venn compl…
12. In a group of 33 students, n(A) = 10, n(B) = 9, and n(A ∩ B) = 2. How many students are in neither A nor B?
33 s · 10 · 9 · 2 · Universal set & Venn compl…

12 questions · Seed 42 · 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 38 students, n(A) = 24, n(B) = 17, and n(A ∩ B) = 11. How many students are in neither A nor B?
8
By inclusion-exclusion, n(A ∪ B) = 24 + 17 − 11 = 30, leaving 38 − 30 = 8 in neither set.
2. In a group of 29 students, n(A) = 9, n(B) = 14, and n(A ∩ B) = 4. How many students are in neither A nor B?
10
By inclusion-exclusion, n(A ∪ B) = 9 + 14 − 4 = 19, leaving 29 − 19 = 10 in neither set.
3. In a group of 38 students, n(A) = 12, n(B) = 17, and n(A ∩ B) = 2. How many students are in neither A nor B?
11
By inclusion-exclusion, n(A ∪ B) = 12 + 17 − 2 = 27, leaving 38 − 27 = 11 in neither set.
4. In a group of 38 students, n(A) = 16, n(B) = 15, and n(A ∩ B) = 4. How many students are in neither A nor B?
11
By inclusion-exclusion, n(A ∪ B) = 16 + 15 − 4 = 27, leaving 38 − 27 = 11 in neither set.
5. In a group of 50 students, n(A) = 23, n(B) = 27, and n(A ∩ B) = 8. How many students are in neither A nor B?
8
By inclusion-exclusion, n(A ∪ B) = 23 + 27 − 8 = 42, leaving 50 − 42 = 8 in neither set.
6. In a group of 30 students, n(A) = 15, n(B) = 7, and n(A ∩ B) = 3. How many students are in neither A nor B?
11
By inclusion-exclusion, n(A ∪ B) = 15 + 7 − 3 = 19, leaving 30 − 19 = 11 in neither set.
7. In a group of 39 students, n(A) = 15, n(B) = 25, and n(A ∩ B) = 7. How many students are in neither A nor B?
6
By inclusion-exclusion, n(A ∪ B) = 15 + 25 − 7 = 33, leaving 39 − 33 = 6 in neither set.
8. In a group of 33 students, n(A) = 20, n(B) = 11, and n(A ∩ B) = 3. How many students are in neither A nor B?
5
By inclusion-exclusion, n(A ∪ B) = 20 + 11 − 3 = 28, leaving 33 − 28 = 5 in neither set.
9. In a group of 39 students, n(A) = 24, n(B) = 11, and n(A ∩ B) = 4. How many students are in neither A nor B?
8
By inclusion-exclusion, n(A ∪ B) = 24 + 11 − 4 = 31, leaving 39 − 31 = 8 in neither set.
10. In a group of 44 students, n(A) = 20, n(B) = 25, and n(A ∩ B) = 11. How many students are in neither A nor B?
10
By inclusion-exclusion, n(A ∪ B) = 20 + 25 − 11 = 34, leaving 44 − 34 = 10 in neither set.
11. In a group of 50 students, n(A) = 24, n(B) = 31, and n(A ∩ B) = 11. How many students are in neither A nor B?
6
By inclusion-exclusion, n(A ∪ B) = 24 + 31 − 11 = 44, leaving 50 − 44 = 6 in neither set.
12. In a group of 33 students, n(A) = 10, n(B) = 9, and n(A ∩ B) = 2. How many students are in neither A nor B?
16
By inclusion-exclusion, n(A ∪ B) = 10 + 9 − 2 = 17, leaving 33 − 17 = 16 in neither set.

12 questions · Seed 42 · Age guidance, not curriculum certification