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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Age band:Ages 13-15 Ages 16-18

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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 48 students, n(A) = 23, n(B) = 19, and n(A ∩ B) = 8. How many students are in neither A nor B?
48 s · 23 · 19 · 8 · Universal set & Venn compl…
2. In a group of 36 students, n(A) = 12, n(B) = 10, and n(A ∩ B) = 3. How many students are in neither A nor B?
36 s · 12 · 10 · 3 · Universal set & Venn compl…
3. In a group of 42 students, n(A) = 13, n(B) = 27, and n(A ∩ B) = 7. How many students are in neither A nor B?
42 s · 13 · 27 · 7 · Universal set & Venn compl…
4. In a group of 33 students, n(A) = 14, n(B) = 17, and n(A ∩ B) = 7. How many students are in neither A nor B?
33 s · 14 · 17 · 7 · Universal set & Venn compl…
5. In a group of 45 students, n(A) = 16, n(B) = 25, and n(A ∩ B) = 5. How many students are in neither A nor B?
45 s · 16 · 25 · 5 · Universal set & Venn compl…
6. In a group of 48 students, n(A) = 15, n(B) = 29, and n(A ∩ B) = 11. How many students are in neither A nor B?
48 s · 15 · 29 · 11 · Universal set & Venn compl…
7. In a group of 41 students, n(A) = 18, n(B) = 22, and n(A ∩ B) = 9. How many students are in neither A nor B?
41 s · 18 · 22 · 9 · Universal set & Venn compl…
8. In a group of 33 students, n(A) = 24, n(B) = 14, and n(A ∩ B) = 9. How many students are in neither A nor B?
33 s · 24 · 14 · 9 · Universal set & Venn compl…
9. In a group of 51 students, n(A) = 25, n(B) = 28, and n(A ∩ B) = 12. How many students are in neither A nor B?
51 s · 25 · 28 · 12 · Universal set & Venn compl…
10. In a group of 28 students, n(A) = 15, n(B) = 15, and n(A ∩ B) = 9. How many students are in neither A nor B?
28 s · 15 · 15 · 9 · Universal set & Venn compl…
11. In a group of 59 students, n(A) = 25, n(B) = 26, and n(A ∩ B) = 6. How many students are in neither A nor B?
59 s · 25 · 26 · 6 · Universal set & Venn compl…
12. In a group of 42 students, n(A) = 9, n(B) = 17, and n(A ∩ B) = 2. How many students are in neither A nor B?
42 s · 9 · 17 · 2 · Universal set & Venn compl…

12 questions · Seed 104729 · 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 48 students, n(A) = 23, n(B) = 19, and n(A ∩ B) = 8. How many students are in neither A nor B?
14
By inclusion-exclusion, n(A ∪ B) = 23 + 19 − 8 = 34, leaving 48 − 34 = 14 in neither set.
2. In a group of 36 students, n(A) = 12, n(B) = 10, and n(A ∩ B) = 3. How many students are in neither A nor B?
17
By inclusion-exclusion, n(A ∪ B) = 12 + 10 − 3 = 19, leaving 36 − 19 = 17 in neither set.
3. In a group of 42 students, n(A) = 13, n(B) = 27, and n(A ∩ B) = 7. How many students are in neither A nor B?
9
By inclusion-exclusion, n(A ∪ B) = 13 + 27 − 7 = 33, leaving 42 − 33 = 9 in neither set.
4. In a group of 33 students, n(A) = 14, n(B) = 17, and n(A ∩ B) = 7. How many students are in neither A nor B?
9
By inclusion-exclusion, n(A ∪ B) = 14 + 17 − 7 = 24, leaving 33 − 24 = 9 in neither set.
5. In a group of 45 students, n(A) = 16, n(B) = 25, and n(A ∩ B) = 5. How many students are in neither A nor B?
9
By inclusion-exclusion, n(A ∪ B) = 16 + 25 − 5 = 36, leaving 45 − 36 = 9 in neither set.
6. In a group of 48 students, n(A) = 15, n(B) = 29, and n(A ∩ B) = 11. How many students are in neither A nor B?
15
By inclusion-exclusion, n(A ∪ B) = 15 + 29 − 11 = 33, leaving 48 − 33 = 15 in neither set.
7. In a group of 41 students, n(A) = 18, n(B) = 22, and n(A ∩ B) = 9. How many students are in neither A nor B?
10
By inclusion-exclusion, n(A ∪ B) = 18 + 22 − 9 = 31, leaving 41 − 31 = 10 in neither set.
8. In a group of 33 students, n(A) = 24, n(B) = 14, and n(A ∩ B) = 9. How many students are in neither A nor B?
4
By inclusion-exclusion, n(A ∪ B) = 24 + 14 − 9 = 29, leaving 33 − 29 = 4 in neither set.
9. In a group of 51 students, n(A) = 25, n(B) = 28, and n(A ∩ B) = 12. How many students are in neither A nor B?
10
By inclusion-exclusion, n(A ∪ B) = 25 + 28 − 12 = 41, leaving 51 − 41 = 10 in neither set.
10. In a group of 28 students, n(A) = 15, n(B) = 15, and n(A ∩ B) = 9. How many students are in neither A nor B?
7
By inclusion-exclusion, n(A ∪ B) = 15 + 15 − 9 = 21, leaving 28 − 21 = 7 in neither set.
11. In a group of 59 students, n(A) = 25, n(B) = 26, and n(A ∩ B) = 6. How many students are in neither A nor B?
14
By inclusion-exclusion, n(A ∪ B) = 25 + 26 − 6 = 45, leaving 59 − 45 = 14 in neither set.
12. In a group of 42 students, n(A) = 9, n(B) = 17, and n(A ∩ B) = 2. How many students are in neither A nor B?
18
By inclusion-exclusion, n(A ∪ B) = 9 + 17 − 2 = 24, leaving 42 − 24 = 18 in neither set.

12 questions · Seed 104729 · 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 48 students, n(A) = 23, n(B) = 19, and n(A ∩ B) = 8. How many students are in neither A nor B?
48 s · 23 · 19 · 8 · Universal set & Venn compl…
2. In a group of 36 students, n(A) = 12, n(B) = 10, and n(A ∩ B) = 3. How many students are in neither A nor B?
36 s · 12 · 10 · 3 · Universal set & Venn compl…
3. In a group of 42 students, n(A) = 13, n(B) = 27, and n(A ∩ B) = 7. How many students are in neither A nor B?
42 s · 13 · 27 · 7 · Universal set & Venn compl…
4. In a group of 33 students, n(A) = 14, n(B) = 17, and n(A ∩ B) = 7. How many students are in neither A nor B?
33 s · 14 · 17 · 7 · Universal set & Venn compl…
5. In a group of 45 students, n(A) = 16, n(B) = 25, and n(A ∩ B) = 5. How many students are in neither A nor B?
45 s · 16 · 25 · 5 · Universal set & Venn compl…
6. In a group of 48 students, n(A) = 15, n(B) = 29, and n(A ∩ B) = 11. How many students are in neither A nor B?
48 s · 15 · 29 · 11 · Universal set & Venn compl…
7. In a group of 41 students, n(A) = 18, n(B) = 22, and n(A ∩ B) = 9. How many students are in neither A nor B?
41 s · 18 · 22 · 9 · Universal set & Venn compl…
8. In a group of 33 students, n(A) = 24, n(B) = 14, and n(A ∩ B) = 9. How many students are in neither A nor B?
33 s · 24 · 14 · 9 · Universal set & Venn compl…
9. In a group of 51 students, n(A) = 25, n(B) = 28, and n(A ∩ B) = 12. How many students are in neither A nor B?
51 s · 25 · 28 · 12 · Universal set & Venn compl…
10. In a group of 28 students, n(A) = 15, n(B) = 15, and n(A ∩ B) = 9. How many students are in neither A nor B?
28 s · 15 · 15 · 9 · Universal set & Venn compl…
11. In a group of 59 students, n(A) = 25, n(B) = 26, and n(A ∩ B) = 6. How many students are in neither A nor B?
59 s · 25 · 26 · 6 · Universal set & Venn compl…
12. In a group of 42 students, n(A) = 9, n(B) = 17, and n(A ∩ B) = 2. How many students are in neither A nor B?
42 s · 9 · 17 · 2 · Universal set & Venn compl…

12 questions · Seed 104729 · 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 48 students, n(A) = 23, n(B) = 19, and n(A ∩ B) = 8. How many students are in neither A nor B?
14
By inclusion-exclusion, n(A ∪ B) = 23 + 19 − 8 = 34, leaving 48 − 34 = 14 in neither set.
2. In a group of 36 students, n(A) = 12, n(B) = 10, and n(A ∩ B) = 3. How many students are in neither A nor B?
17
By inclusion-exclusion, n(A ∪ B) = 12 + 10 − 3 = 19, leaving 36 − 19 = 17 in neither set.
3. In a group of 42 students, n(A) = 13, n(B) = 27, and n(A ∩ B) = 7. How many students are in neither A nor B?
9
By inclusion-exclusion, n(A ∪ B) = 13 + 27 − 7 = 33, leaving 42 − 33 = 9 in neither set.
4. In a group of 33 students, n(A) = 14, n(B) = 17, and n(A ∩ B) = 7. How many students are in neither A nor B?
9
By inclusion-exclusion, n(A ∪ B) = 14 + 17 − 7 = 24, leaving 33 − 24 = 9 in neither set.
5. In a group of 45 students, n(A) = 16, n(B) = 25, and n(A ∩ B) = 5. How many students are in neither A nor B?
9
By inclusion-exclusion, n(A ∪ B) = 16 + 25 − 5 = 36, leaving 45 − 36 = 9 in neither set.
6. In a group of 48 students, n(A) = 15, n(B) = 29, and n(A ∩ B) = 11. How many students are in neither A nor B?
15
By inclusion-exclusion, n(A ∪ B) = 15 + 29 − 11 = 33, leaving 48 − 33 = 15 in neither set.
7. In a group of 41 students, n(A) = 18, n(B) = 22, and n(A ∩ B) = 9. How many students are in neither A nor B?
10
By inclusion-exclusion, n(A ∪ B) = 18 + 22 − 9 = 31, leaving 41 − 31 = 10 in neither set.
8. In a group of 33 students, n(A) = 24, n(B) = 14, and n(A ∩ B) = 9. How many students are in neither A nor B?
4
By inclusion-exclusion, n(A ∪ B) = 24 + 14 − 9 = 29, leaving 33 − 29 = 4 in neither set.
9. In a group of 51 students, n(A) = 25, n(B) = 28, and n(A ∩ B) = 12. How many students are in neither A nor B?
10
By inclusion-exclusion, n(A ∪ B) = 25 + 28 − 12 = 41, leaving 51 − 41 = 10 in neither set.
10. In a group of 28 students, n(A) = 15, n(B) = 15, and n(A ∩ B) = 9. How many students are in neither A nor B?
7
By inclusion-exclusion, n(A ∪ B) = 15 + 15 − 9 = 21, leaving 28 − 21 = 7 in neither set.
11. In a group of 59 students, n(A) = 25, n(B) = 26, and n(A ∩ B) = 6. How many students are in neither A nor B?
14
By inclusion-exclusion, n(A ∪ B) = 25 + 26 − 6 = 45, leaving 59 − 45 = 14 in neither set.
12. In a group of 42 students, n(A) = 9, n(B) = 17, and n(A ∩ B) = 2. How many students are in neither A nor B?
18
By inclusion-exclusion, n(A ∪ B) = 9 + 17 − 2 = 24, leaving 42 − 24 = 18 in neither set.

12 questions · Seed 104729 · Age guidance, not curriculum certification