ReasoningAges 16-18

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 16-18

Universal set & Venn complements

Take your time. Show your thinking.

1. In a group of 46 students, n(A) = 30, n(B) = 14, and n(A ∩ B) = 10. How many students are in neither A nor B?
46 s · 30 · 14 · 10 · Universal set & Venn compl…
2. In a group of 43 students, n(A) = 19, n(B) = 22, and n(A ∩ B) = 2. How many students are in neither A nor B?
43 s · 19 · 22 · 2 · Universal set & Venn compl…
3. In a group of 54 students, n(A) = 29, n(B) = 31, and n(A ∩ B) = 12. How many students are in neither A nor B?
54 s · 29 · 31 · 12 · Universal set & Venn compl…
4. In a group of 48 students, n(A) = 25, n(B) = 25, and n(A ∩ B) = 8. How many students are in neither A nor B?
48 s · 25 · 25 · 8 · Universal set & Venn compl…
5. In a group of 52 students, n(A) = 25, n(B) = 24, and n(A ∩ B) = 9. How many students are in neither A nor B?
52 s · 25 · 24 · 9 · Universal set & Venn compl…
6. In a group of 42 students, n(A) = 18, n(B) = 26, and n(A ∩ B) = 7. How many students are in neither A nor B?
42 s · 18 · 26 · 7 · Universal set & Venn compl…
7. In a group of 34 students, n(A) = 10, n(B) = 22, and n(A ∩ B) = 5. How many students are in neither A nor B?
34 s · 10 · 22 · 5 · Universal set & Venn compl…
8. In a group of 46 students, n(A) = 27, n(B) = 23, and n(A ∩ B) = 11. How many students are in neither A nor B?
46 s · 27 · 23 · 11 · Universal set & Venn compl…
9. In a group of 47 students, n(A) = 17, n(B) = 25, and n(A ∩ B) = 5. How many students are in neither A nor B?
47 s · 17 · 25 · 5 · Universal set & Venn compl…
10. In a group of 32 students, n(A) = 18, n(B) = 16, and n(A ∩ B) = 8. How many students are in neither A nor B?
32 s · 18 · 16 · 8 · Universal set & Venn compl…
11. In a group of 30 students, n(A) = 9, n(B) = 16, and n(A ∩ B) = 2. How many students are in neither A nor B?
30 s · 9 · 16 · 2 · Universal set & Venn compl…
12. In a group of 49 students, n(A) = 28, n(B) = 20, and n(A ∩ B) = 10. How many students are in neither A nor B?
49 s · 28 · 20 · 10 · Universal set & Venn compl…

12 questions · Seed 48 · Age guidance, not curriculum certification

View the answer key

Worksheet StudioAnswer key · Ages 16-18

Universal set & Venn complements

Answers and reasoning. Review before teaching.

1. In a group of 46 students, n(A) = 30, n(B) = 14, and n(A ∩ B) = 10. How many students are in neither A nor B?
12
By inclusion-exclusion, n(A ∪ B) = 30 + 14 − 10 = 34, leaving 46 − 34 = 12 in neither set.
2. In a group of 43 students, n(A) = 19, n(B) = 22, and n(A ∩ B) = 2. How many students are in neither A nor B?
4
By inclusion-exclusion, n(A ∪ B) = 19 + 22 − 2 = 39, leaving 43 − 39 = 4 in neither set.
3. In a group of 54 students, n(A) = 29, n(B) = 31, and n(A ∩ B) = 12. How many students are in neither A nor B?
6
By inclusion-exclusion, n(A ∪ B) = 29 + 31 − 12 = 48, leaving 54 − 48 = 6 in neither set.
4. In a group of 48 students, n(A) = 25, n(B) = 25, and n(A ∩ B) = 8. How many students are in neither A nor B?
6
By inclusion-exclusion, n(A ∪ B) = 25 + 25 − 8 = 42, leaving 48 − 42 = 6 in neither set.
5. In a group of 52 students, n(A) = 25, n(B) = 24, and n(A ∩ B) = 9. How many students are in neither A nor B?
12
By inclusion-exclusion, n(A ∪ B) = 25 + 24 − 9 = 40, leaving 52 − 40 = 12 in neither set.
6. In a group of 42 students, n(A) = 18, n(B) = 26, and n(A ∩ B) = 7. How many students are in neither A nor B?
5
By inclusion-exclusion, n(A ∪ B) = 18 + 26 − 7 = 37, leaving 42 − 37 = 5 in neither set.
7. In a group of 34 students, n(A) = 10, n(B) = 22, and n(A ∩ B) = 5. How many students are in neither A nor B?
7
By inclusion-exclusion, n(A ∪ B) = 10 + 22 − 5 = 27, leaving 34 − 27 = 7 in neither set.
8. In a group of 46 students, n(A) = 27, n(B) = 23, and n(A ∩ B) = 11. How many students are in neither A nor B?
7
By inclusion-exclusion, n(A ∪ B) = 27 + 23 − 11 = 39, leaving 46 − 39 = 7 in neither set.
9. In a group of 47 students, n(A) = 17, n(B) = 25, and n(A ∩ B) = 5. How many students are in neither A nor B?
10
By inclusion-exclusion, n(A ∪ B) = 17 + 25 − 5 = 37, leaving 47 − 37 = 10 in neither set.
10. In a group of 32 students, n(A) = 18, n(B) = 16, and n(A ∩ B) = 8. How many students are in neither A nor B?
6
By inclusion-exclusion, n(A ∪ B) = 18 + 16 − 8 = 26, leaving 32 − 26 = 6 in neither set.
11. In a group of 30 students, n(A) = 9, n(B) = 16, and n(A ∩ B) = 2. How many students are in neither A nor B?
7
By inclusion-exclusion, n(A ∪ B) = 9 + 16 − 2 = 23, leaving 30 − 23 = 7 in neither set.
12. In a group of 49 students, n(A) = 28, n(B) = 20, and n(A ∩ B) = 10. How many students are in neither A nor B?
11
By inclusion-exclusion, n(A ∪ B) = 28 + 20 − 10 = 38, leaving 49 − 38 = 11 in neither set.

12 questions · Seed 48 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 16-18

Universal set & Venn complements

Take your time. Show your thinking.

1. In a group of 46 students, n(A) = 30, n(B) = 14, and n(A ∩ B) = 10. How many students are in neither A nor B?
46 s · 30 · 14 · 10 · Universal set & Venn compl…
2. In a group of 43 students, n(A) = 19, n(B) = 22, and n(A ∩ B) = 2. How many students are in neither A nor B?
43 s · 19 · 22 · 2 · Universal set & Venn compl…
3. In a group of 54 students, n(A) = 29, n(B) = 31, and n(A ∩ B) = 12. How many students are in neither A nor B?
54 s · 29 · 31 · 12 · Universal set & Venn compl…
4. In a group of 48 students, n(A) = 25, n(B) = 25, and n(A ∩ B) = 8. How many students are in neither A nor B?
48 s · 25 · 25 · 8 · Universal set & Venn compl…
5. In a group of 52 students, n(A) = 25, n(B) = 24, and n(A ∩ B) = 9. How many students are in neither A nor B?
52 s · 25 · 24 · 9 · Universal set & Venn compl…
6. In a group of 42 students, n(A) = 18, n(B) = 26, and n(A ∩ B) = 7. How many students are in neither A nor B?
42 s · 18 · 26 · 7 · Universal set & Venn compl…
7. In a group of 34 students, n(A) = 10, n(B) = 22, and n(A ∩ B) = 5. How many students are in neither A nor B?
34 s · 10 · 22 · 5 · Universal set & Venn compl…
8. In a group of 46 students, n(A) = 27, n(B) = 23, and n(A ∩ B) = 11. How many students are in neither A nor B?
46 s · 27 · 23 · 11 · Universal set & Venn compl…
9. In a group of 47 students, n(A) = 17, n(B) = 25, and n(A ∩ B) = 5. How many students are in neither A nor B?
47 s · 17 · 25 · 5 · Universal set & Venn compl…
10. In a group of 32 students, n(A) = 18, n(B) = 16, and n(A ∩ B) = 8. How many students are in neither A nor B?
32 s · 18 · 16 · 8 · Universal set & Venn compl…
11. In a group of 30 students, n(A) = 9, n(B) = 16, and n(A ∩ B) = 2. How many students are in neither A nor B?
30 s · 9 · 16 · 2 · Universal set & Venn compl…
12. In a group of 49 students, n(A) = 28, n(B) = 20, and n(A ∩ B) = 10. How many students are in neither A nor B?
49 s · 28 · 20 · 10 · Universal set & Venn compl…

12 questions · Seed 48 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 16-18

Universal set & Venn complements

Answers and reasoning. Review before teaching.

1. In a group of 46 students, n(A) = 30, n(B) = 14, and n(A ∩ B) = 10. How many students are in neither A nor B?
12
By inclusion-exclusion, n(A ∪ B) = 30 + 14 − 10 = 34, leaving 46 − 34 = 12 in neither set.
2. In a group of 43 students, n(A) = 19, n(B) = 22, and n(A ∩ B) = 2. How many students are in neither A nor B?
4
By inclusion-exclusion, n(A ∪ B) = 19 + 22 − 2 = 39, leaving 43 − 39 = 4 in neither set.
3. In a group of 54 students, n(A) = 29, n(B) = 31, and n(A ∩ B) = 12. How many students are in neither A nor B?
6
By inclusion-exclusion, n(A ∪ B) = 29 + 31 − 12 = 48, leaving 54 − 48 = 6 in neither set.
4. In a group of 48 students, n(A) = 25, n(B) = 25, and n(A ∩ B) = 8. How many students are in neither A nor B?
6
By inclusion-exclusion, n(A ∪ B) = 25 + 25 − 8 = 42, leaving 48 − 42 = 6 in neither set.
5. In a group of 52 students, n(A) = 25, n(B) = 24, and n(A ∩ B) = 9. How many students are in neither A nor B?
12
By inclusion-exclusion, n(A ∪ B) = 25 + 24 − 9 = 40, leaving 52 − 40 = 12 in neither set.
6. In a group of 42 students, n(A) = 18, n(B) = 26, and n(A ∩ B) = 7. How many students are in neither A nor B?
5
By inclusion-exclusion, n(A ∪ B) = 18 + 26 − 7 = 37, leaving 42 − 37 = 5 in neither set.
7. In a group of 34 students, n(A) = 10, n(B) = 22, and n(A ∩ B) = 5. How many students are in neither A nor B?
7
By inclusion-exclusion, n(A ∪ B) = 10 + 22 − 5 = 27, leaving 34 − 27 = 7 in neither set.
8. In a group of 46 students, n(A) = 27, n(B) = 23, and n(A ∩ B) = 11. How many students are in neither A nor B?
7
By inclusion-exclusion, n(A ∪ B) = 27 + 23 − 11 = 39, leaving 46 − 39 = 7 in neither set.
9. In a group of 47 students, n(A) = 17, n(B) = 25, and n(A ∩ B) = 5. How many students are in neither A nor B?
10
By inclusion-exclusion, n(A ∪ B) = 17 + 25 − 5 = 37, leaving 47 − 37 = 10 in neither set.
10. In a group of 32 students, n(A) = 18, n(B) = 16, and n(A ∩ B) = 8. How many students are in neither A nor B?
6
By inclusion-exclusion, n(A ∪ B) = 18 + 16 − 8 = 26, leaving 32 − 26 = 6 in neither set.
11. In a group of 30 students, n(A) = 9, n(B) = 16, and n(A ∩ B) = 2. How many students are in neither A nor B?
7
By inclusion-exclusion, n(A ∪ B) = 9 + 16 − 2 = 23, leaving 30 − 23 = 7 in neither set.
12. In a group of 49 students, n(A) = 28, n(B) = 20, and n(A ∩ B) = 10. How many students are in neither A nor B?
11
By inclusion-exclusion, n(A ∪ B) = 28 + 20 − 10 = 38, leaving 49 − 38 = 11 in neither set.

12 questions · Seed 48 · Age guidance, not curriculum certification