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 42 students, n(A) = 14, n(B) = 19, and n(A ∩ B) = 4. How many students are in neither A nor B?
42 s · 14 · 19 · 4 · Universal set & Venn compl…
2. In a group of 38 students, n(A) = 16, n(B) = 18, and n(A ∩ B) = 9. How many students are in neither A nor B?
38 s · 16 · 18 · 9 · Universal set & Venn compl…
3. In a group of 30 students, n(A) = 17, n(B) = 15, and n(A ∩ B) = 7. How many students are in neither A nor B?
30 s · 17 · 15 · 7 · Universal set & Venn compl…
4. In a group of 43 students, n(A) = 14, n(B) = 23, and n(A ∩ B) = 3. How many students are in neither A nor B?
43 s · 14 · 23 · 3 · Universal set & Venn compl…
5. In a group of 33 students, n(A) = 13, n(B) = 23, and n(A ∩ B) = 8. How many students are in neither A nor B?
33 s · 13 · 23 · 8 · Universal set & Venn compl…
6. In a group of 27 students, n(A) = 13, n(B) = 9, and n(A ∩ B) = 4. How many students are in neither A nor B?
27 s · 13 · 9 · 4 · Universal set & Venn compl…
7. In a group of 24 students, n(A) = 15, n(B) = 8, and n(A ∩ B) = 3. How many students are in neither A nor B?
24 s · 15 · 8 · 3 · Universal set & Venn compl…
8. In a group of 52 students, n(A) = 30, n(B) = 28, and n(A ∩ B) = 10. How many students are in neither A nor B?
52 s · 30 · 28 · 10 · Universal set & Venn compl…
9. In a group of 55 students, n(A) = 19, n(B) = 29, and n(A ∩ B) = 11. How many students are in neither A nor B?
55 s · 19 · 29 · 11 · Universal set & Venn compl…
10. In a group of 51 students, n(A) = 21, n(B) = 30, and n(A ∩ B) = 12. How many students are in neither A nor B?
51 s · 21 · 30 · 12 · Universal set & Venn compl…
11. In a group of 47 students, n(A) = 14, n(B) = 27, and n(A ∩ B) = 9. How many students are in neither A nor B?
47 s · 14 · 27 · 9 · Universal set & Venn compl…
12. In a group of 46 students, n(A) = 16, n(B) = 16, and n(A ∩ B) = 2. How many students are in neither A nor B?
46 s · 16 · 16 · 2 · Universal set & Venn compl…

12 questions · Seed 104731 · 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 42 students, n(A) = 14, n(B) = 19, and n(A ∩ B) = 4. How many students are in neither A nor B?
13
By inclusion-exclusion, n(A ∪ B) = 14 + 19 − 4 = 29, leaving 42 − 29 = 13 in neither set.
2. In a group of 38 students, n(A) = 16, n(B) = 18, and n(A ∩ B) = 9. How many students are in neither A nor B?
13
By inclusion-exclusion, n(A ∪ B) = 16 + 18 − 9 = 25, leaving 38 − 25 = 13 in neither set.
3. In a group of 30 students, n(A) = 17, n(B) = 15, and n(A ∩ B) = 7. How many students are in neither A nor B?
5
By inclusion-exclusion, n(A ∪ B) = 17 + 15 − 7 = 25, leaving 30 − 25 = 5 in neither set.
4. In a group of 43 students, n(A) = 14, n(B) = 23, and n(A ∩ B) = 3. How many students are in neither A nor B?
9
By inclusion-exclusion, n(A ∪ B) = 14 + 23 − 3 = 34, leaving 43 − 34 = 9 in neither set.
5. In a group of 33 students, n(A) = 13, n(B) = 23, and n(A ∩ B) = 8. How many students are in neither A nor B?
5
By inclusion-exclusion, n(A ∪ B) = 13 + 23 − 8 = 28, leaving 33 − 28 = 5 in neither set.
6. In a group of 27 students, n(A) = 13, n(B) = 9, and n(A ∩ B) = 4. How many students are in neither A nor B?
9
By inclusion-exclusion, n(A ∪ B) = 13 + 9 − 4 = 18, leaving 27 − 18 = 9 in neither set.
7. In a group of 24 students, n(A) = 15, n(B) = 8, and n(A ∩ B) = 3. How many students are in neither A nor B?
4
By inclusion-exclusion, n(A ∪ B) = 15 + 8 − 3 = 20, leaving 24 − 20 = 4 in neither set.
8. In a group of 52 students, n(A) = 30, n(B) = 28, and n(A ∩ B) = 10. How many students are in neither A nor B?
4
By inclusion-exclusion, n(A ∪ B) = 30 + 28 − 10 = 48, leaving 52 − 48 = 4 in neither set.
9. In a group of 55 students, n(A) = 19, n(B) = 29, and n(A ∩ B) = 11. How many students are in neither A nor B?
18
By inclusion-exclusion, n(A ∪ B) = 19 + 29 − 11 = 37, leaving 55 − 37 = 18 in neither set.
10. In a group of 51 students, n(A) = 21, n(B) = 30, and n(A ∩ B) = 12. How many students are in neither A nor B?
12
By inclusion-exclusion, n(A ∪ B) = 21 + 30 − 12 = 39, leaving 51 − 39 = 12 in neither set.
11. In a group of 47 students, n(A) = 14, n(B) = 27, and n(A ∩ B) = 9. How many students are in neither A nor B?
15
By inclusion-exclusion, n(A ∪ B) = 14 + 27 − 9 = 32, leaving 47 − 32 = 15 in neither set.
12. In a group of 46 students, n(A) = 16, n(B) = 16, and n(A ∩ B) = 2. How many students are in neither A nor B?
16
By inclusion-exclusion, n(A ∪ B) = 16 + 16 − 2 = 30, leaving 46 − 30 = 16 in neither set.

12 questions · Seed 104731 · 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 42 students, n(A) = 14, n(B) = 19, and n(A ∩ B) = 4. How many students are in neither A nor B?
42 s · 14 · 19 · 4 · Universal set & Venn compl…
2. In a group of 38 students, n(A) = 16, n(B) = 18, and n(A ∩ B) = 9. How many students are in neither A nor B?
38 s · 16 · 18 · 9 · Universal set & Venn compl…
3. In a group of 30 students, n(A) = 17, n(B) = 15, and n(A ∩ B) = 7. How many students are in neither A nor B?
30 s · 17 · 15 · 7 · Universal set & Venn compl…
4. In a group of 43 students, n(A) = 14, n(B) = 23, and n(A ∩ B) = 3. How many students are in neither A nor B?
43 s · 14 · 23 · 3 · Universal set & Venn compl…
5. In a group of 33 students, n(A) = 13, n(B) = 23, and n(A ∩ B) = 8. How many students are in neither A nor B?
33 s · 13 · 23 · 8 · Universal set & Venn compl…
6. In a group of 27 students, n(A) = 13, n(B) = 9, and n(A ∩ B) = 4. How many students are in neither A nor B?
27 s · 13 · 9 · 4 · Universal set & Venn compl…
7. In a group of 24 students, n(A) = 15, n(B) = 8, and n(A ∩ B) = 3. How many students are in neither A nor B?
24 s · 15 · 8 · 3 · Universal set & Venn compl…
8. In a group of 52 students, n(A) = 30, n(B) = 28, and n(A ∩ B) = 10. How many students are in neither A nor B?
52 s · 30 · 28 · 10 · Universal set & Venn compl…
9. In a group of 55 students, n(A) = 19, n(B) = 29, and n(A ∩ B) = 11. How many students are in neither A nor B?
55 s · 19 · 29 · 11 · Universal set & Venn compl…
10. In a group of 51 students, n(A) = 21, n(B) = 30, and n(A ∩ B) = 12. How many students are in neither A nor B?
51 s · 21 · 30 · 12 · Universal set & Venn compl…
11. In a group of 47 students, n(A) = 14, n(B) = 27, and n(A ∩ B) = 9. How many students are in neither A nor B?
47 s · 14 · 27 · 9 · Universal set & Venn compl…
12. In a group of 46 students, n(A) = 16, n(B) = 16, and n(A ∩ B) = 2. How many students are in neither A nor B?
46 s · 16 · 16 · 2 · Universal set & Venn compl…

12 questions · Seed 104731 · 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 42 students, n(A) = 14, n(B) = 19, and n(A ∩ B) = 4. How many students are in neither A nor B?
13
By inclusion-exclusion, n(A ∪ B) = 14 + 19 − 4 = 29, leaving 42 − 29 = 13 in neither set.
2. In a group of 38 students, n(A) = 16, n(B) = 18, and n(A ∩ B) = 9. How many students are in neither A nor B?
13
By inclusion-exclusion, n(A ∪ B) = 16 + 18 − 9 = 25, leaving 38 − 25 = 13 in neither set.
3. In a group of 30 students, n(A) = 17, n(B) = 15, and n(A ∩ B) = 7. How many students are in neither A nor B?
5
By inclusion-exclusion, n(A ∪ B) = 17 + 15 − 7 = 25, leaving 30 − 25 = 5 in neither set.
4. In a group of 43 students, n(A) = 14, n(B) = 23, and n(A ∩ B) = 3. How many students are in neither A nor B?
9
By inclusion-exclusion, n(A ∪ B) = 14 + 23 − 3 = 34, leaving 43 − 34 = 9 in neither set.
5. In a group of 33 students, n(A) = 13, n(B) = 23, and n(A ∩ B) = 8. How many students are in neither A nor B?
5
By inclusion-exclusion, n(A ∪ B) = 13 + 23 − 8 = 28, leaving 33 − 28 = 5 in neither set.
6. In a group of 27 students, n(A) = 13, n(B) = 9, and n(A ∩ B) = 4. How many students are in neither A nor B?
9
By inclusion-exclusion, n(A ∪ B) = 13 + 9 − 4 = 18, leaving 27 − 18 = 9 in neither set.
7. In a group of 24 students, n(A) = 15, n(B) = 8, and n(A ∩ B) = 3. How many students are in neither A nor B?
4
By inclusion-exclusion, n(A ∪ B) = 15 + 8 − 3 = 20, leaving 24 − 20 = 4 in neither set.
8. In a group of 52 students, n(A) = 30, n(B) = 28, and n(A ∩ B) = 10. How many students are in neither A nor B?
4
By inclusion-exclusion, n(A ∪ B) = 30 + 28 − 10 = 48, leaving 52 − 48 = 4 in neither set.
9. In a group of 55 students, n(A) = 19, n(B) = 29, and n(A ∩ B) = 11. How many students are in neither A nor B?
18
By inclusion-exclusion, n(A ∪ B) = 19 + 29 − 11 = 37, leaving 55 − 37 = 18 in neither set.
10. In a group of 51 students, n(A) = 21, n(B) = 30, and n(A ∩ B) = 12. How many students are in neither A nor B?
12
By inclusion-exclusion, n(A ∪ B) = 21 + 30 − 12 = 39, leaving 51 − 39 = 12 in neither set.
11. In a group of 47 students, n(A) = 14, n(B) = 27, and n(A ∩ B) = 9. How many students are in neither A nor B?
15
By inclusion-exclusion, n(A ∪ B) = 14 + 27 − 9 = 32, leaving 47 − 32 = 15 in neither set.
12. In a group of 46 students, n(A) = 16, n(B) = 16, and n(A ∩ B) = 2. How many students are in neither A nor B?
16
By inclusion-exclusion, n(A ∪ B) = 16 + 16 − 2 = 30, leaving 46 − 30 = 16 in neither set.

12 questions · Seed 104731 · Age guidance, not curriculum certification