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.

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Worksheet StudioPractice pack · Ages 13-15

Universal set & Venn complements

Take your time. Show your thinking.

1. In a group of 34 students, n(A) = 10, n(B) = 17, and n(A ∩ B) = 5. How many students are in neither A nor B?
34 s · 10 · 17 · 5 · Universal set & Venn compl…
2. In a group of 28 students, n(A) = 17, n(B) = 18, and n(A ∩ B) = 11. How many students are in neither A nor B?
28 s · 17 · 18 · 11 · Universal set & Venn compl…
3. In a group of 32 students, n(A) = 9, n(B) = 19, and n(A ∩ B) = 3. How many students are in neither A nor B?
32 s · 9 · 19 · 3 · Universal set & Venn compl…
4. In a group of 31 students, n(A) = 7, n(B) = 19, and n(A ∩ B) = 2. How many students are in neither A nor B?
31 s · 7 · 19 · 2 · Universal set & Venn compl…
5. In a group of 29 students, n(A) = 12, n(B) = 15, and n(A ∩ B) = 5. How many students are in neither A nor B?
29 s · 12 · 15 · 5 · Universal set & Venn compl…
6. In a group of 61 students, n(A) = 29, n(B) = 24, and n(A ∩ B) = 9. How many students are in neither A nor B?
61 s · 29 · 24 · 9 · Universal set & Venn compl…
7. In a group of 54 students, n(A) = 22, n(B) = 27, and n(A ∩ B) = 7. How many students are in neither A nor B?
54 s · 22 · 27 · 7 · Universal set & Venn compl…
8. In a group of 55 students, n(A) = 24, n(B) = 19, and n(A ∩ B) = 6. How many students are in neither A nor B?
55 s · 24 · 19 · 6 · Universal set & Venn compl…
9. In a group of 39 students, n(A) = 20, n(B) = 7, and n(A ∩ B) = 3. How many students are in neither A nor B?
39 s · 20 · 7 · 3 · Universal set & Venn compl…
10. In a group of 56 students, n(A) = 18, n(B) = 31, and n(A ∩ B) = 11. How many students are in neither A nor B?
56 s · 18 · 31 · 11 · Universal set & Venn compl…
11. In a group of 34 students, n(A) = 20, n(B) = 13, and n(A ∩ B) = 9. How many students are in neither A nor B?
34 s · 20 · 13 · 9 · Universal set & Venn compl…
12. In a group of 40 students, n(A) = 16, n(B) = 19, and n(A ∩ B) = 2. How many students are in neither A nor B?
40 s · 16 · 19 · 2 · Universal set & Venn compl…

12 questions · Seed 43 · 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 34 students, n(A) = 10, n(B) = 17, and n(A ∩ B) = 5. How many students are in neither A nor B?
12
By inclusion-exclusion, n(A ∪ B) = 10 + 17 − 5 = 22, leaving 34 − 22 = 12 in neither set.
2. In a group of 28 students, n(A) = 17, n(B) = 18, and n(A ∩ B) = 11. How many students are in neither A nor B?
4
By inclusion-exclusion, n(A ∪ B) = 17 + 18 − 11 = 24, leaving 28 − 24 = 4 in neither set.
3. In a group of 32 students, n(A) = 9, n(B) = 19, and n(A ∩ B) = 3. How many students are in neither A nor B?
7
By inclusion-exclusion, n(A ∪ B) = 9 + 19 − 3 = 25, leaving 32 − 25 = 7 in neither set.
4. In a group of 31 students, n(A) = 7, n(B) = 19, and n(A ∩ B) = 2. How many students are in neither A nor B?
7
By inclusion-exclusion, n(A ∪ B) = 7 + 19 − 2 = 24, leaving 31 − 24 = 7 in neither set.
5. In a group of 29 students, n(A) = 12, n(B) = 15, and n(A ∩ B) = 5. How many students are in neither A nor B?
7
By inclusion-exclusion, n(A ∪ B) = 12 + 15 − 5 = 22, leaving 29 − 22 = 7 in neither set.
6. In a group of 61 students, n(A) = 29, n(B) = 24, and n(A ∩ B) = 9. How many students are in neither A nor B?
17
By inclusion-exclusion, n(A ∪ B) = 29 + 24 − 9 = 44, leaving 61 − 44 = 17 in neither set.
7. In a group of 54 students, n(A) = 22, n(B) = 27, and n(A ∩ B) = 7. How many students are in neither A nor B?
12
By inclusion-exclusion, n(A ∪ B) = 22 + 27 − 7 = 42, leaving 54 − 42 = 12 in neither set.
8. In a group of 55 students, n(A) = 24, n(B) = 19, and n(A ∩ B) = 6. How many students are in neither A nor B?
18
By inclusion-exclusion, n(A ∪ B) = 24 + 19 − 6 = 37, leaving 55 − 37 = 18 in neither set.
9. In a group of 39 students, n(A) = 20, n(B) = 7, and n(A ∩ B) = 3. How many students are in neither A nor B?
15
By inclusion-exclusion, n(A ∪ B) = 20 + 7 − 3 = 24, leaving 39 − 24 = 15 in neither set.
10. In a group of 56 students, n(A) = 18, n(B) = 31, and n(A ∩ B) = 11. How many students are in neither A nor B?
18
By inclusion-exclusion, n(A ∪ B) = 18 + 31 − 11 = 38, leaving 56 − 38 = 18 in neither set.
11. In a group of 34 students, n(A) = 20, n(B) = 13, and n(A ∩ B) = 9. How many students are in neither A nor B?
10
By inclusion-exclusion, n(A ∪ B) = 20 + 13 − 9 = 24, leaving 34 − 24 = 10 in neither set.
12. In a group of 40 students, n(A) = 16, n(B) = 19, and n(A ∩ B) = 2. How many students are in neither A nor B?
7
By inclusion-exclusion, n(A ∪ B) = 16 + 19 − 2 = 33, leaving 40 − 33 = 7 in neither set.

12 questions · Seed 43 · 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 34 students, n(A) = 10, n(B) = 17, and n(A ∩ B) = 5. How many students are in neither A nor B?
34 s · 10 · 17 · 5 · Universal set & Venn compl…
2. In a group of 28 students, n(A) = 17, n(B) = 18, and n(A ∩ B) = 11. How many students are in neither A nor B?
28 s · 17 · 18 · 11 · Universal set & Venn compl…
3. In a group of 32 students, n(A) = 9, n(B) = 19, and n(A ∩ B) = 3. How many students are in neither A nor B?
32 s · 9 · 19 · 3 · Universal set & Venn compl…
4. In a group of 31 students, n(A) = 7, n(B) = 19, and n(A ∩ B) = 2. How many students are in neither A nor B?
31 s · 7 · 19 · 2 · Universal set & Venn compl…
5. In a group of 29 students, n(A) = 12, n(B) = 15, and n(A ∩ B) = 5. How many students are in neither A nor B?
29 s · 12 · 15 · 5 · Universal set & Venn compl…
6. In a group of 61 students, n(A) = 29, n(B) = 24, and n(A ∩ B) = 9. How many students are in neither A nor B?
61 s · 29 · 24 · 9 · Universal set & Venn compl…
7. In a group of 54 students, n(A) = 22, n(B) = 27, and n(A ∩ B) = 7. How many students are in neither A nor B?
54 s · 22 · 27 · 7 · Universal set & Venn compl…
8. In a group of 55 students, n(A) = 24, n(B) = 19, and n(A ∩ B) = 6. How many students are in neither A nor B?
55 s · 24 · 19 · 6 · Universal set & Venn compl…
9. In a group of 39 students, n(A) = 20, n(B) = 7, and n(A ∩ B) = 3. How many students are in neither A nor B?
39 s · 20 · 7 · 3 · Universal set & Venn compl…
10. In a group of 56 students, n(A) = 18, n(B) = 31, and n(A ∩ B) = 11. How many students are in neither A nor B?
56 s · 18 · 31 · 11 · Universal set & Venn compl…
11. In a group of 34 students, n(A) = 20, n(B) = 13, and n(A ∩ B) = 9. How many students are in neither A nor B?
34 s · 20 · 13 · 9 · Universal set & Venn compl…
12. In a group of 40 students, n(A) = 16, n(B) = 19, and n(A ∩ B) = 2. How many students are in neither A nor B?
40 s · 16 · 19 · 2 · Universal set & Venn compl…

12 questions · Seed 43 · 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 34 students, n(A) = 10, n(B) = 17, and n(A ∩ B) = 5. How many students are in neither A nor B?
12
By inclusion-exclusion, n(A ∪ B) = 10 + 17 − 5 = 22, leaving 34 − 22 = 12 in neither set.
2. In a group of 28 students, n(A) = 17, n(B) = 18, and n(A ∩ B) = 11. How many students are in neither A nor B?
4
By inclusion-exclusion, n(A ∪ B) = 17 + 18 − 11 = 24, leaving 28 − 24 = 4 in neither set.
3. In a group of 32 students, n(A) = 9, n(B) = 19, and n(A ∩ B) = 3. How many students are in neither A nor B?
7
By inclusion-exclusion, n(A ∪ B) = 9 + 19 − 3 = 25, leaving 32 − 25 = 7 in neither set.
4. In a group of 31 students, n(A) = 7, n(B) = 19, and n(A ∩ B) = 2. How many students are in neither A nor B?
7
By inclusion-exclusion, n(A ∪ B) = 7 + 19 − 2 = 24, leaving 31 − 24 = 7 in neither set.
5. In a group of 29 students, n(A) = 12, n(B) = 15, and n(A ∩ B) = 5. How many students are in neither A nor B?
7
By inclusion-exclusion, n(A ∪ B) = 12 + 15 − 5 = 22, leaving 29 − 22 = 7 in neither set.
6. In a group of 61 students, n(A) = 29, n(B) = 24, and n(A ∩ B) = 9. How many students are in neither A nor B?
17
By inclusion-exclusion, n(A ∪ B) = 29 + 24 − 9 = 44, leaving 61 − 44 = 17 in neither set.
7. In a group of 54 students, n(A) = 22, n(B) = 27, and n(A ∩ B) = 7. How many students are in neither A nor B?
12
By inclusion-exclusion, n(A ∪ B) = 22 + 27 − 7 = 42, leaving 54 − 42 = 12 in neither set.
8. In a group of 55 students, n(A) = 24, n(B) = 19, and n(A ∩ B) = 6. How many students are in neither A nor B?
18
By inclusion-exclusion, n(A ∪ B) = 24 + 19 − 6 = 37, leaving 55 − 37 = 18 in neither set.
9. In a group of 39 students, n(A) = 20, n(B) = 7, and n(A ∩ B) = 3. How many students are in neither A nor B?
15
By inclusion-exclusion, n(A ∪ B) = 20 + 7 − 3 = 24, leaving 39 − 24 = 15 in neither set.
10. In a group of 56 students, n(A) = 18, n(B) = 31, and n(A ∩ B) = 11. How many students are in neither A nor B?
18
By inclusion-exclusion, n(A ∪ B) = 18 + 31 − 11 = 38, leaving 56 − 38 = 18 in neither set.
11. In a group of 34 students, n(A) = 20, n(B) = 13, and n(A ∩ B) = 9. How many students are in neither A nor B?
10
By inclusion-exclusion, n(A ∪ B) = 20 + 13 − 9 = 24, leaving 34 − 24 = 10 in neither set.
12. In a group of 40 students, n(A) = 16, n(B) = 19, and n(A ∩ B) = 2. How many students are in neither A nor B?
7
By inclusion-exclusion, n(A ∪ B) = 16 + 19 − 2 = 33, leaving 40 − 33 = 7 in neither set.

12 questions · Seed 43 · Age guidance, not curriculum certification