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 43 students, n(A) = 23, n(B) = 26, and n(A ∩ B) = 10. How many students are in neither A nor B?
43 s · 23 · 26 · 10 · Universal set & Venn compl…
2. In a group of 44 students, n(A) = 22, n(B) = 18, and n(A ∩ B) = 5. How many students are in neither A nor B?
44 s · 22 · 18 · 5 · Universal set & Venn compl…
3. In a group of 53 students, n(A) = 19, n(B) = 28, and n(A ∩ B) = 10. How many students are in neither A nor B?
53 s · 19 · 28 · 10 · Universal set & Venn compl…
4. In a group of 58 students, n(A) = 27, n(B) = 27, and n(A ∩ B) = 12. How many students are in neither A nor B?
58 s · 27 · 27 · 12 · Universal set & Venn compl…
5. In a group of 52 students, n(A) = 24, n(B) = 24, and n(A ∩ B) = 10. How many students are in neither A nor B?
52 s · 24 · 24 · 10 · Universal set & Venn compl…
6. In a group of 28 students, n(A) = 12, n(B) = 21, and n(A ∩ B) = 8. How many students are in neither A nor B?
28 s · 12 · 21 · 8 · Universal set & Venn compl…
7. In a group of 32 students, n(A) = 16, n(B) = 14, and n(A ∩ B) = 3. How many students are in neither A nor B?
32 s · 16 · 14 · 3 · Universal set & Venn compl…
8. In a group of 45 students, n(A) = 19, n(B) = 21, and n(A ∩ B) = 5. How many students are in neither A nor B?
45 s · 19 · 21 · 5 · Universal set & Venn compl…
9. In a group of 53 students, n(A) = 26, n(B) = 19, and n(A ∩ B) = 7. How many students are in neither A nor B?
53 s · 26 · 19 · 7 · Universal set & Venn compl…
10. In a group of 41 students, n(A) = 10, n(B) = 18, and n(A ∩ B) = 5. How many students are in neither A nor B?
41 s · 10 · 18 · 5 · Universal set & Venn compl…
11. In a group of 58 students, n(A) = 24, n(B) = 31, and n(A ∩ B) = 12. How many students are in neither A nor B?
58 s · 24 · 31 · 12 · Universal set & Venn compl…
12. In a group of 31 students, n(A) = 17, n(B) = 13, and n(A ∩ B) = 6. How many students are in neither A nor B?
31 s · 17 · 13 · 6 · Universal set & Venn compl…

12 questions · Seed 104735 · 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 43 students, n(A) = 23, n(B) = 26, and n(A ∩ B) = 10. How many students are in neither A nor B?
4
By inclusion-exclusion, n(A ∪ B) = 23 + 26 − 10 = 39, leaving 43 − 39 = 4 in neither set.
2. In a group of 44 students, n(A) = 22, n(B) = 18, and n(A ∩ B) = 5. How many students are in neither A nor B?
9
By inclusion-exclusion, n(A ∪ B) = 22 + 18 − 5 = 35, leaving 44 − 35 = 9 in neither set.
3. In a group of 53 students, n(A) = 19, n(B) = 28, and n(A ∩ B) = 10. How many students are in neither A nor B?
16
By inclusion-exclusion, n(A ∪ B) = 19 + 28 − 10 = 37, leaving 53 − 37 = 16 in neither set.
4. In a group of 58 students, n(A) = 27, n(B) = 27, and n(A ∩ B) = 12. How many students are in neither A nor B?
16
By inclusion-exclusion, n(A ∪ B) = 27 + 27 − 12 = 42, leaving 58 − 42 = 16 in neither set.
5. In a group of 52 students, n(A) = 24, n(B) = 24, and n(A ∩ B) = 10. How many students are in neither A nor B?
14
By inclusion-exclusion, n(A ∪ B) = 24 + 24 − 10 = 38, leaving 52 − 38 = 14 in neither set.
6. In a group of 28 students, n(A) = 12, n(B) = 21, and n(A ∩ B) = 8. How many students are in neither A nor B?
3
By inclusion-exclusion, n(A ∪ B) = 12 + 21 − 8 = 25, leaving 28 − 25 = 3 in neither set.
7. In a group of 32 students, n(A) = 16, n(B) = 14, and n(A ∩ B) = 3. How many students are in neither A nor B?
5
By inclusion-exclusion, n(A ∪ B) = 16 + 14 − 3 = 27, leaving 32 − 27 = 5 in neither set.
8. In a group of 45 students, n(A) = 19, n(B) = 21, and n(A ∩ B) = 5. How many students are in neither A nor B?
10
By inclusion-exclusion, n(A ∪ B) = 19 + 21 − 5 = 35, leaving 45 − 35 = 10 in neither set.
9. In a group of 53 students, n(A) = 26, n(B) = 19, and n(A ∩ B) = 7. How many students are in neither A nor B?
15
By inclusion-exclusion, n(A ∪ B) = 26 + 19 − 7 = 38, leaving 53 − 38 = 15 in neither set.
10. In a group of 41 students, n(A) = 10, n(B) = 18, and n(A ∩ B) = 5. How many students are in neither A nor B?
18
By inclusion-exclusion, n(A ∪ B) = 10 + 18 − 5 = 23, leaving 41 − 23 = 18 in neither set.
11. In a group of 58 students, n(A) = 24, n(B) = 31, and n(A ∩ B) = 12. How many students are in neither A nor B?
15
By inclusion-exclusion, n(A ∪ B) = 24 + 31 − 12 = 43, leaving 58 − 43 = 15 in neither set.
12. In a group of 31 students, n(A) = 17, n(B) = 13, and n(A ∩ B) = 6. How many students are in neither A nor B?
7
By inclusion-exclusion, n(A ∪ B) = 17 + 13 − 6 = 24, leaving 31 − 24 = 7 in neither set.

12 questions · Seed 104735 · 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 43 students, n(A) = 23, n(B) = 26, and n(A ∩ B) = 10. How many students are in neither A nor B?
43 s · 23 · 26 · 10 · Universal set & Venn compl…
2. In a group of 44 students, n(A) = 22, n(B) = 18, and n(A ∩ B) = 5. How many students are in neither A nor B?
44 s · 22 · 18 · 5 · Universal set & Venn compl…
3. In a group of 53 students, n(A) = 19, n(B) = 28, and n(A ∩ B) = 10. How many students are in neither A nor B?
53 s · 19 · 28 · 10 · Universal set & Venn compl…
4. In a group of 58 students, n(A) = 27, n(B) = 27, and n(A ∩ B) = 12. How many students are in neither A nor B?
58 s · 27 · 27 · 12 · Universal set & Venn compl…
5. In a group of 52 students, n(A) = 24, n(B) = 24, and n(A ∩ B) = 10. How many students are in neither A nor B?
52 s · 24 · 24 · 10 · Universal set & Venn compl…
6. In a group of 28 students, n(A) = 12, n(B) = 21, and n(A ∩ B) = 8. How many students are in neither A nor B?
28 s · 12 · 21 · 8 · Universal set & Venn compl…
7. In a group of 32 students, n(A) = 16, n(B) = 14, and n(A ∩ B) = 3. How many students are in neither A nor B?
32 s · 16 · 14 · 3 · Universal set & Venn compl…
8. In a group of 45 students, n(A) = 19, n(B) = 21, and n(A ∩ B) = 5. How many students are in neither A nor B?
45 s · 19 · 21 · 5 · Universal set & Venn compl…
9. In a group of 53 students, n(A) = 26, n(B) = 19, and n(A ∩ B) = 7. How many students are in neither A nor B?
53 s · 26 · 19 · 7 · Universal set & Venn compl…
10. In a group of 41 students, n(A) = 10, n(B) = 18, and n(A ∩ B) = 5. How many students are in neither A nor B?
41 s · 10 · 18 · 5 · Universal set & Venn compl…
11. In a group of 58 students, n(A) = 24, n(B) = 31, and n(A ∩ B) = 12. How many students are in neither A nor B?
58 s · 24 · 31 · 12 · Universal set & Venn compl…
12. In a group of 31 students, n(A) = 17, n(B) = 13, and n(A ∩ B) = 6. How many students are in neither A nor B?
31 s · 17 · 13 · 6 · Universal set & Venn compl…

12 questions · Seed 104735 · 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 43 students, n(A) = 23, n(B) = 26, and n(A ∩ B) = 10. How many students are in neither A nor B?
4
By inclusion-exclusion, n(A ∪ B) = 23 + 26 − 10 = 39, leaving 43 − 39 = 4 in neither set.
2. In a group of 44 students, n(A) = 22, n(B) = 18, and n(A ∩ B) = 5. How many students are in neither A nor B?
9
By inclusion-exclusion, n(A ∪ B) = 22 + 18 − 5 = 35, leaving 44 − 35 = 9 in neither set.
3. In a group of 53 students, n(A) = 19, n(B) = 28, and n(A ∩ B) = 10. How many students are in neither A nor B?
16
By inclusion-exclusion, n(A ∪ B) = 19 + 28 − 10 = 37, leaving 53 − 37 = 16 in neither set.
4. In a group of 58 students, n(A) = 27, n(B) = 27, and n(A ∩ B) = 12. How many students are in neither A nor B?
16
By inclusion-exclusion, n(A ∪ B) = 27 + 27 − 12 = 42, leaving 58 − 42 = 16 in neither set.
5. In a group of 52 students, n(A) = 24, n(B) = 24, and n(A ∩ B) = 10. How many students are in neither A nor B?
14
By inclusion-exclusion, n(A ∪ B) = 24 + 24 − 10 = 38, leaving 52 − 38 = 14 in neither set.
6. In a group of 28 students, n(A) = 12, n(B) = 21, and n(A ∩ B) = 8. How many students are in neither A nor B?
3
By inclusion-exclusion, n(A ∪ B) = 12 + 21 − 8 = 25, leaving 28 − 25 = 3 in neither set.
7. In a group of 32 students, n(A) = 16, n(B) = 14, and n(A ∩ B) = 3. How many students are in neither A nor B?
5
By inclusion-exclusion, n(A ∪ B) = 16 + 14 − 3 = 27, leaving 32 − 27 = 5 in neither set.
8. In a group of 45 students, n(A) = 19, n(B) = 21, and n(A ∩ B) = 5. How many students are in neither A nor B?
10
By inclusion-exclusion, n(A ∪ B) = 19 + 21 − 5 = 35, leaving 45 − 35 = 10 in neither set.
9. In a group of 53 students, n(A) = 26, n(B) = 19, and n(A ∩ B) = 7. How many students are in neither A nor B?
15
By inclusion-exclusion, n(A ∪ B) = 26 + 19 − 7 = 38, leaving 53 − 38 = 15 in neither set.
10. In a group of 41 students, n(A) = 10, n(B) = 18, and n(A ∩ B) = 5. How many students are in neither A nor B?
18
By inclusion-exclusion, n(A ∪ B) = 10 + 18 − 5 = 23, leaving 41 − 23 = 18 in neither set.
11. In a group of 58 students, n(A) = 24, n(B) = 31, and n(A ∩ B) = 12. How many students are in neither A nor B?
15
By inclusion-exclusion, n(A ∪ B) = 24 + 31 − 12 = 43, leaving 58 − 43 = 15 in neither set.
12. In a group of 31 students, n(A) = 17, n(B) = 13, and n(A ∩ B) = 6. How many students are in neither A nor B?
7
By inclusion-exclusion, n(A ∪ B) = 17 + 13 − 6 = 24, leaving 31 − 24 = 7 in neither set.

12 questions · Seed 104735 · Age guidance, not curriculum certification