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 35 students, n(A) = 18, n(B) = 16, and n(A ∩ B) = 9. How many students are in neither A nor B?
35 s · 18 · 16 · 9 · Universal set & Venn compl…
2. In a group of 48 students, n(A) = 28, n(B) = 27, and n(A ∩ B) = 10. How many students are in neither A nor B?
48 s · 28 · 27 · 10 · Universal set & Venn compl…
3. In a group of 47 students, n(A) = 23, n(B) = 14, and n(A ∩ B) = 5. How many students are in neither A nor B?
47 s · 23 · 14 · 5 · Universal set & Venn compl…
4. In a group of 38 students, n(A) = 21, n(B) = 16, and n(A ∩ B) = 8. How many students are in neither A nor B?
38 s · 21 · 16 · 8 · Universal set & Venn compl…
5. In a group of 35 students, n(A) = 23, n(B) = 20, and n(A ∩ B) = 12. How many students are in neither A nor B?
35 s · 23 · 20 · 12 · Universal set & Venn compl…
6. In a group of 30 students, n(A) = 11, n(B) = 13, and n(A ∩ B) = 7. How many students are in neither A nor B?
30 s · 11 · 13 · 7 · Universal set & Venn compl…
7. In a group of 33 students, n(A) = 14, n(B) = 13, and n(A ∩ B) = 3. How many students are in neither A nor B?
33 s · 14 · 13 · 3 · Universal set & Venn compl…
8. In a group of 31 students, n(A) = 12, n(B) = 16, and n(A ∩ B) = 4. How many students are in neither A nor B?
31 s · 12 · 16 · 4 · Universal set & Venn compl…
9. In a group of 54 students, n(A) = 28, n(B) = 22, and n(A ∩ B) = 10. How many students are in neither A nor B?
54 s · 28 · 22 · 10 · Universal set & Venn compl…
10. In a group of 51 students, n(A) = 27, n(B) = 27, and n(A ∩ B) = 11. How many students are in neither A nor B?
51 s · 27 · 27 · 11 · Universal set & Venn compl…
11. In a group of 33 students, n(A) = 8, n(B) = 21, and n(A ∩ B) = 3. How many students are in neither A nor B?
33 s · 8 · 21 · 3 · Universal set & Venn compl…
12. In a group of 34 students, n(A) = 17, n(B) = 22, and n(A ∩ B) = 12. How many students are in neither A nor B?
34 s · 17 · 22 · 12 · Universal set & Venn compl…

12 questions · Seed 104732 · 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 35 students, n(A) = 18, n(B) = 16, and n(A ∩ B) = 9. How many students are in neither A nor B?
10
By inclusion-exclusion, n(A ∪ B) = 18 + 16 − 9 = 25, leaving 35 − 25 = 10 in neither set.
2. In a group of 48 students, n(A) = 28, n(B) = 27, and n(A ∩ B) = 10. How many students are in neither A nor B?
3
By inclusion-exclusion, n(A ∪ B) = 28 + 27 − 10 = 45, leaving 48 − 45 = 3 in neither set.
3. In a group of 47 students, n(A) = 23, n(B) = 14, and n(A ∩ B) = 5. How many students are in neither A nor B?
15
By inclusion-exclusion, n(A ∪ B) = 23 + 14 − 5 = 32, leaving 47 − 32 = 15 in neither set.
4. In a group of 38 students, n(A) = 21, n(B) = 16, and n(A ∩ B) = 8. How many students are in neither A nor B?
9
By inclusion-exclusion, n(A ∪ B) = 21 + 16 − 8 = 29, leaving 38 − 29 = 9 in neither set.
5. In a group of 35 students, n(A) = 23, n(B) = 20, and n(A ∩ B) = 12. How many students are in neither A nor B?
4
By inclusion-exclusion, n(A ∪ B) = 23 + 20 − 12 = 31, leaving 35 − 31 = 4 in neither set.
6. In a group of 30 students, n(A) = 11, n(B) = 13, and n(A ∩ B) = 7. How many students are in neither A nor B?
13
By inclusion-exclusion, n(A ∪ B) = 11 + 13 − 7 = 17, leaving 30 − 17 = 13 in neither set.
7. In a group of 33 students, n(A) = 14, n(B) = 13, and n(A ∩ B) = 3. How many students are in neither A nor B?
9
By inclusion-exclusion, n(A ∪ B) = 14 + 13 − 3 = 24, leaving 33 − 24 = 9 in neither set.
8. In a group of 31 students, n(A) = 12, n(B) = 16, and n(A ∩ B) = 4. How many students are in neither A nor B?
7
By inclusion-exclusion, n(A ∪ B) = 12 + 16 − 4 = 24, leaving 31 − 24 = 7 in neither set.
9. In a group of 54 students, n(A) = 28, n(B) = 22, and n(A ∩ B) = 10. How many students are in neither A nor B?
14
By inclusion-exclusion, n(A ∪ B) = 28 + 22 − 10 = 40, leaving 54 − 40 = 14 in neither set.
10. In a group of 51 students, n(A) = 27, n(B) = 27, and n(A ∩ B) = 11. How many students are in neither A nor B?
8
By inclusion-exclusion, n(A ∪ B) = 27 + 27 − 11 = 43, leaving 51 − 43 = 8 in neither set.
11. In a group of 33 students, n(A) = 8, n(B) = 21, and n(A ∩ B) = 3. How many students are in neither A nor B?
7
By inclusion-exclusion, n(A ∪ B) = 8 + 21 − 3 = 26, leaving 33 − 26 = 7 in neither set.
12. In a group of 34 students, n(A) = 17, n(B) = 22, and n(A ∩ B) = 12. How many students are in neither A nor B?
7
By inclusion-exclusion, n(A ∪ B) = 17 + 22 − 12 = 27, leaving 34 − 27 = 7 in neither set.

12 questions · Seed 104732 · 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 35 students, n(A) = 18, n(B) = 16, and n(A ∩ B) = 9. How many students are in neither A nor B?
35 s · 18 · 16 · 9 · Universal set & Venn compl…
2. In a group of 48 students, n(A) = 28, n(B) = 27, and n(A ∩ B) = 10. How many students are in neither A nor B?
48 s · 28 · 27 · 10 · Universal set & Venn compl…
3. In a group of 47 students, n(A) = 23, n(B) = 14, and n(A ∩ B) = 5. How many students are in neither A nor B?
47 s · 23 · 14 · 5 · Universal set & Venn compl…
4. In a group of 38 students, n(A) = 21, n(B) = 16, and n(A ∩ B) = 8. How many students are in neither A nor B?
38 s · 21 · 16 · 8 · Universal set & Venn compl…
5. In a group of 35 students, n(A) = 23, n(B) = 20, and n(A ∩ B) = 12. How many students are in neither A nor B?
35 s · 23 · 20 · 12 · Universal set & Venn compl…
6. In a group of 30 students, n(A) = 11, n(B) = 13, and n(A ∩ B) = 7. How many students are in neither A nor B?
30 s · 11 · 13 · 7 · Universal set & Venn compl…
7. In a group of 33 students, n(A) = 14, n(B) = 13, and n(A ∩ B) = 3. How many students are in neither A nor B?
33 s · 14 · 13 · 3 · Universal set & Venn compl…
8. In a group of 31 students, n(A) = 12, n(B) = 16, and n(A ∩ B) = 4. How many students are in neither A nor B?
31 s · 12 · 16 · 4 · Universal set & Venn compl…
9. In a group of 54 students, n(A) = 28, n(B) = 22, and n(A ∩ B) = 10. How many students are in neither A nor B?
54 s · 28 · 22 · 10 · Universal set & Venn compl…
10. In a group of 51 students, n(A) = 27, n(B) = 27, and n(A ∩ B) = 11. How many students are in neither A nor B?
51 s · 27 · 27 · 11 · Universal set & Venn compl…
11. In a group of 33 students, n(A) = 8, n(B) = 21, and n(A ∩ B) = 3. How many students are in neither A nor B?
33 s · 8 · 21 · 3 · Universal set & Venn compl…
12. In a group of 34 students, n(A) = 17, n(B) = 22, and n(A ∩ B) = 12. How many students are in neither A nor B?
34 s · 17 · 22 · 12 · Universal set & Venn compl…

12 questions · Seed 104732 · 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 35 students, n(A) = 18, n(B) = 16, and n(A ∩ B) = 9. How many students are in neither A nor B?
10
By inclusion-exclusion, n(A ∪ B) = 18 + 16 − 9 = 25, leaving 35 − 25 = 10 in neither set.
2. In a group of 48 students, n(A) = 28, n(B) = 27, and n(A ∩ B) = 10. How many students are in neither A nor B?
3
By inclusion-exclusion, n(A ∪ B) = 28 + 27 − 10 = 45, leaving 48 − 45 = 3 in neither set.
3. In a group of 47 students, n(A) = 23, n(B) = 14, and n(A ∩ B) = 5. How many students are in neither A nor B?
15
By inclusion-exclusion, n(A ∪ B) = 23 + 14 − 5 = 32, leaving 47 − 32 = 15 in neither set.
4. In a group of 38 students, n(A) = 21, n(B) = 16, and n(A ∩ B) = 8. How many students are in neither A nor B?
9
By inclusion-exclusion, n(A ∪ B) = 21 + 16 − 8 = 29, leaving 38 − 29 = 9 in neither set.
5. In a group of 35 students, n(A) = 23, n(B) = 20, and n(A ∩ B) = 12. How many students are in neither A nor B?
4
By inclusion-exclusion, n(A ∪ B) = 23 + 20 − 12 = 31, leaving 35 − 31 = 4 in neither set.
6. In a group of 30 students, n(A) = 11, n(B) = 13, and n(A ∩ B) = 7. How many students are in neither A nor B?
13
By inclusion-exclusion, n(A ∪ B) = 11 + 13 − 7 = 17, leaving 30 − 17 = 13 in neither set.
7. In a group of 33 students, n(A) = 14, n(B) = 13, and n(A ∩ B) = 3. How many students are in neither A nor B?
9
By inclusion-exclusion, n(A ∪ B) = 14 + 13 − 3 = 24, leaving 33 − 24 = 9 in neither set.
8. In a group of 31 students, n(A) = 12, n(B) = 16, and n(A ∩ B) = 4. How many students are in neither A nor B?
7
By inclusion-exclusion, n(A ∪ B) = 12 + 16 − 4 = 24, leaving 31 − 24 = 7 in neither set.
9. In a group of 54 students, n(A) = 28, n(B) = 22, and n(A ∩ B) = 10. How many students are in neither A nor B?
14
By inclusion-exclusion, n(A ∪ B) = 28 + 22 − 10 = 40, leaving 54 − 40 = 14 in neither set.
10. In a group of 51 students, n(A) = 27, n(B) = 27, and n(A ∩ B) = 11. How many students are in neither A nor B?
8
By inclusion-exclusion, n(A ∪ B) = 27 + 27 − 11 = 43, leaving 51 − 43 = 8 in neither set.
11. In a group of 33 students, n(A) = 8, n(B) = 21, and n(A ∩ B) = 3. How many students are in neither A nor B?
7
By inclusion-exclusion, n(A ∪ B) = 8 + 21 − 3 = 26, leaving 33 − 26 = 7 in neither set.
12. In a group of 34 students, n(A) = 17, n(B) = 22, and n(A ∩ B) = 12. How many students are in neither A nor B?
7
By inclusion-exclusion, n(A ∪ B) = 17 + 22 − 12 = 27, leaving 34 − 27 = 7 in neither set.

12 questions · Seed 104732 · Age guidance, not curriculum certification