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 51 students, n(A) = 26, n(B) = 23, and n(A ∩ B) = 6. How many students are in neither A nor B?
51 s · 26 · 23 · 6 · Universal set & Venn compl…
2. In a group of 62 students, n(A) = 29, n(B) = 28, and n(A ∩ B) = 12. How many students are in neither A nor B?
62 s · 29 · 28 · 12 · Universal set & Venn compl…
3. In a group of 48 students, n(A) = 16, n(B) = 27, and n(A ∩ B) = 7. How many students are in neither A nor B?
48 s · 16 · 27 · 7 · Universal set & Venn compl…
4. In a group of 44 students, n(A) = 20, n(B) = 14, and n(A ∩ B) = 5. How many students are in neither A nor B?
44 s · 20 · 14 · 5 · Universal set & Venn compl…
5. In a group of 36 students, n(A) = 19, n(B) = 23, and n(A ∩ B) = 12. How many students are in neither A nor B?
36 s · 19 · 23 · 12 · Universal set & Venn compl…
6. In a group of 35 students, n(A) = 19, n(B) = 15, and n(A ∩ B) = 4. How many students are in neither A nor B?
35 s · 19 · 15 · 4 · Universal set & Venn compl…
7. In a group of 51 students, n(A) = 27, n(B) = 30, and n(A ∩ B) = 12. How many students are in neither A nor B?
51 s · 27 · 30 · 12 · Universal set & Venn compl…
8. In a group of 34 students, n(A) = 12, n(B) = 13, and n(A ∩ B) = 2. How many students are in neither A nor B?
34 s · 12 · 13 · 2 · Universal set & Venn compl…
9. In a group of 41 students, n(A) = 27, n(B) = 18, and n(A ∩ B) = 7. How many students are in neither A nor B?
41 s · 27 · 18 · 7 · Universal set & Venn compl…
10. In a group of 35 students, n(A) = 16, n(B) = 14, and n(A ∩ B) = 8. How many students are in neither A nor B?
35 s · 16 · 14 · 8 · Universal set & Venn compl…
11. In a group of 40 students, n(A) = 18, n(B) = 20, and n(A ∩ B) = 12. How many students are in neither A nor B?
40 s · 18 · 20 · 12 · Universal set & Venn compl…
12. In a group of 57 students, n(A) = 27, n(B) = 27, and n(A ∩ B) = 12. How many students are in neither A nor B?
57 s · 27 · 27 · 12 · Universal set & Venn compl…

12 questions · Seed 104737 · 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 51 students, n(A) = 26, n(B) = 23, and n(A ∩ B) = 6. How many students are in neither A nor B?
8
By inclusion-exclusion, n(A ∪ B) = 26 + 23 − 6 = 43, leaving 51 − 43 = 8 in neither set.
2. In a group of 62 students, n(A) = 29, n(B) = 28, and n(A ∩ B) = 12. How many students are in neither A nor B?
17
By inclusion-exclusion, n(A ∪ B) = 29 + 28 − 12 = 45, leaving 62 − 45 = 17 in neither set.
3. In a group of 48 students, n(A) = 16, n(B) = 27, and n(A ∩ B) = 7. How many students are in neither A nor B?
12
By inclusion-exclusion, n(A ∪ B) = 16 + 27 − 7 = 36, leaving 48 − 36 = 12 in neither set.
4. In a group of 44 students, n(A) = 20, n(B) = 14, and n(A ∩ B) = 5. How many students are in neither A nor B?
15
By inclusion-exclusion, n(A ∪ B) = 20 + 14 − 5 = 29, leaving 44 − 29 = 15 in neither set.
5. In a group of 36 students, n(A) = 19, n(B) = 23, and n(A ∩ B) = 12. How many students are in neither A nor B?
6
By inclusion-exclusion, n(A ∪ B) = 19 + 23 − 12 = 30, leaving 36 − 30 = 6 in neither set.
6. In a group of 35 students, n(A) = 19, n(B) = 15, and n(A ∩ B) = 4. How many students are in neither A nor B?
5
By inclusion-exclusion, n(A ∪ B) = 19 + 15 − 4 = 30, leaving 35 − 30 = 5 in neither set.
7. In a group of 51 students, n(A) = 27, n(B) = 30, and n(A ∩ B) = 12. How many students are in neither A nor B?
6
By inclusion-exclusion, n(A ∪ B) = 27 + 30 − 12 = 45, leaving 51 − 45 = 6 in neither set.
8. In a group of 34 students, n(A) = 12, n(B) = 13, and n(A ∩ B) = 2. How many students are in neither A nor B?
11
By inclusion-exclusion, n(A ∪ B) = 12 + 13 − 2 = 23, leaving 34 − 23 = 11 in neither set.
9. In a group of 41 students, n(A) = 27, n(B) = 18, and n(A ∩ B) = 7. How many students are in neither A nor B?
3
By inclusion-exclusion, n(A ∪ B) = 27 + 18 − 7 = 38, leaving 41 − 38 = 3 in neither set.
10. In a group of 35 students, n(A) = 16, n(B) = 14, and n(A ∩ B) = 8. How many students are in neither A nor B?
13
By inclusion-exclusion, n(A ∪ B) = 16 + 14 − 8 = 22, leaving 35 − 22 = 13 in neither set.
11. In a group of 40 students, n(A) = 18, n(B) = 20, and n(A ∩ B) = 12. How many students are in neither A nor B?
14
By inclusion-exclusion, n(A ∪ B) = 18 + 20 − 12 = 26, leaving 40 − 26 = 14 in neither set.
12. In a group of 57 students, n(A) = 27, n(B) = 27, and n(A ∩ B) = 12. How many students are in neither A nor B?
15
By inclusion-exclusion, n(A ∪ B) = 27 + 27 − 12 = 42, leaving 57 − 42 = 15 in neither set.

12 questions · Seed 104737 · 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 51 students, n(A) = 26, n(B) = 23, and n(A ∩ B) = 6. How many students are in neither A nor B?
51 s · 26 · 23 · 6 · Universal set & Venn compl…
2. In a group of 62 students, n(A) = 29, n(B) = 28, and n(A ∩ B) = 12. How many students are in neither A nor B?
62 s · 29 · 28 · 12 · Universal set & Venn compl…
3. In a group of 48 students, n(A) = 16, n(B) = 27, and n(A ∩ B) = 7. How many students are in neither A nor B?
48 s · 16 · 27 · 7 · Universal set & Venn compl…
4. In a group of 44 students, n(A) = 20, n(B) = 14, and n(A ∩ B) = 5. How many students are in neither A nor B?
44 s · 20 · 14 · 5 · Universal set & Venn compl…
5. In a group of 36 students, n(A) = 19, n(B) = 23, and n(A ∩ B) = 12. How many students are in neither A nor B?
36 s · 19 · 23 · 12 · Universal set & Venn compl…
6. In a group of 35 students, n(A) = 19, n(B) = 15, and n(A ∩ B) = 4. How many students are in neither A nor B?
35 s · 19 · 15 · 4 · Universal set & Venn compl…
7. In a group of 51 students, n(A) = 27, n(B) = 30, and n(A ∩ B) = 12. How many students are in neither A nor B?
51 s · 27 · 30 · 12 · Universal set & Venn compl…
8. In a group of 34 students, n(A) = 12, n(B) = 13, and n(A ∩ B) = 2. How many students are in neither A nor B?
34 s · 12 · 13 · 2 · Universal set & Venn compl…
9. In a group of 41 students, n(A) = 27, n(B) = 18, and n(A ∩ B) = 7. How many students are in neither A nor B?
41 s · 27 · 18 · 7 · Universal set & Venn compl…
10. In a group of 35 students, n(A) = 16, n(B) = 14, and n(A ∩ B) = 8. How many students are in neither A nor B?
35 s · 16 · 14 · 8 · Universal set & Venn compl…
11. In a group of 40 students, n(A) = 18, n(B) = 20, and n(A ∩ B) = 12. How many students are in neither A nor B?
40 s · 18 · 20 · 12 · Universal set & Venn compl…
12. In a group of 57 students, n(A) = 27, n(B) = 27, and n(A ∩ B) = 12. How many students are in neither A nor B?
57 s · 27 · 27 · 12 · Universal set & Venn compl…

12 questions · Seed 104737 · 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 51 students, n(A) = 26, n(B) = 23, and n(A ∩ B) = 6. How many students are in neither A nor B?
8
By inclusion-exclusion, n(A ∪ B) = 26 + 23 − 6 = 43, leaving 51 − 43 = 8 in neither set.
2. In a group of 62 students, n(A) = 29, n(B) = 28, and n(A ∩ B) = 12. How many students are in neither A nor B?
17
By inclusion-exclusion, n(A ∪ B) = 29 + 28 − 12 = 45, leaving 62 − 45 = 17 in neither set.
3. In a group of 48 students, n(A) = 16, n(B) = 27, and n(A ∩ B) = 7. How many students are in neither A nor B?
12
By inclusion-exclusion, n(A ∪ B) = 16 + 27 − 7 = 36, leaving 48 − 36 = 12 in neither set.
4. In a group of 44 students, n(A) = 20, n(B) = 14, and n(A ∩ B) = 5. How many students are in neither A nor B?
15
By inclusion-exclusion, n(A ∪ B) = 20 + 14 − 5 = 29, leaving 44 − 29 = 15 in neither set.
5. In a group of 36 students, n(A) = 19, n(B) = 23, and n(A ∩ B) = 12. How many students are in neither A nor B?
6
By inclusion-exclusion, n(A ∪ B) = 19 + 23 − 12 = 30, leaving 36 − 30 = 6 in neither set.
6. In a group of 35 students, n(A) = 19, n(B) = 15, and n(A ∩ B) = 4. How many students are in neither A nor B?
5
By inclusion-exclusion, n(A ∪ B) = 19 + 15 − 4 = 30, leaving 35 − 30 = 5 in neither set.
7. In a group of 51 students, n(A) = 27, n(B) = 30, and n(A ∩ B) = 12. How many students are in neither A nor B?
6
By inclusion-exclusion, n(A ∪ B) = 27 + 30 − 12 = 45, leaving 51 − 45 = 6 in neither set.
8. In a group of 34 students, n(A) = 12, n(B) = 13, and n(A ∩ B) = 2. How many students are in neither A nor B?
11
By inclusion-exclusion, n(A ∪ B) = 12 + 13 − 2 = 23, leaving 34 − 23 = 11 in neither set.
9. In a group of 41 students, n(A) = 27, n(B) = 18, and n(A ∩ B) = 7. How many students are in neither A nor B?
3
By inclusion-exclusion, n(A ∪ B) = 27 + 18 − 7 = 38, leaving 41 − 38 = 3 in neither set.
10. In a group of 35 students, n(A) = 16, n(B) = 14, and n(A ∩ B) = 8. How many students are in neither A nor B?
13
By inclusion-exclusion, n(A ∪ B) = 16 + 14 − 8 = 22, leaving 35 − 22 = 13 in neither set.
11. In a group of 40 students, n(A) = 18, n(B) = 20, and n(A ∩ B) = 12. How many students are in neither A nor B?
14
By inclusion-exclusion, n(A ∪ B) = 18 + 20 − 12 = 26, leaving 40 − 26 = 14 in neither set.
12. In a group of 57 students, n(A) = 27, n(B) = 27, and n(A ∩ B) = 12. How many students are in neither A nor B?
15
By inclusion-exclusion, n(A ∪ B) = 27 + 27 − 12 = 42, leaving 57 − 42 = 15 in neither set.

12 questions · Seed 104737 · Age guidance, not curriculum certification