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 40 students, n(A) = 28, n(B) = 18, and n(A ∩ B) = 11. How many students are in neither A nor B?
40 s · 28 · 18 · 11 · Universal set & Venn compl…
2. In a group of 33 students, n(A) = 14, n(B) = 14, and n(A ∩ B) = 6. How many students are in neither A nor B?
33 s · 14 · 14 · 6 · Universal set & Venn compl…
3. In a group of 59 students, n(A) = 25, n(B) = 29, and n(A ∩ B) = 9. How many students are in neither A nor B?
59 s · 25 · 29 · 9 · Universal set & Venn compl…
4. In a group of 48 students, n(A) = 29, n(B) = 20, and n(A ∩ B) = 9. How many students are in neither A nor B?
48 s · 29 · 20 · 9 · Universal set & Venn compl…
5. In a group of 39 students, n(A) = 18, n(B) = 16, and n(A ∩ B) = 5. How many students are in neither A nor B?
39 s · 18 · 16 · 5 · Universal set & Venn compl…
6. In a group of 45 students, n(A) = 28, n(B) = 19, and n(A ∩ B) = 9. How many students are in neither A nor B?
45 s · 28 · 19 · 9 · Universal set & Venn compl…
7. In a group of 44 students, n(A) = 12, n(B) = 17, and n(A ∩ B) = 3. How many students are in neither A nor B?
44 s · 12 · 17 · 3 · Universal set & Venn compl…
8. In a group of 58 students, n(A) = 31, n(B) = 28, and n(A ∩ B) = 12. How many students are in neither A nor B?
58 s · 31 · 28 · 12 · Universal set & Venn compl…
9. In a group of 42 students, n(A) = 21, n(B) = 13, and n(A ∩ B) = 2. How many students are in neither A nor B?
42 s · 21 · 13 · 2 · Universal set & Venn compl…
10. In a group of 36 students, n(A) = 17, n(B) = 18, and n(A ∩ B) = 10. How many students are in neither A nor B?
36 s · 17 · 18 · 10 · Universal set & Venn compl…
11. In a group of 43 students, n(A) = 28, n(B) = 18, and n(A ∩ B) = 11. How many students are in neither A nor B?
43 s · 28 · 18 · 11 · Universal set & Venn compl…
12. In a group of 50 students, n(A) = 22, n(B) = 19, and n(A ∩ B) = 3. How many students are in neither A nor B?
50 s · 22 · 19 · 3 · Universal set & Venn compl…

12 questions · Seed 104733 · 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 40 students, n(A) = 28, n(B) = 18, and n(A ∩ B) = 11. How many students are in neither A nor B?
5
By inclusion-exclusion, n(A ∪ B) = 28 + 18 − 11 = 35, leaving 40 − 35 = 5 in neither set.
2. In a group of 33 students, n(A) = 14, n(B) = 14, and n(A ∩ B) = 6. How many students are in neither A nor B?
11
By inclusion-exclusion, n(A ∪ B) = 14 + 14 − 6 = 22, leaving 33 − 22 = 11 in neither set.
3. In a group of 59 students, n(A) = 25, n(B) = 29, and n(A ∩ B) = 9. How many students are in neither A nor B?
14
By inclusion-exclusion, n(A ∪ B) = 25 + 29 − 9 = 45, leaving 59 − 45 = 14 in neither set.
4. In a group of 48 students, n(A) = 29, n(B) = 20, and n(A ∩ B) = 9. How many students are in neither A nor B?
8
By inclusion-exclusion, n(A ∪ B) = 29 + 20 − 9 = 40, leaving 48 − 40 = 8 in neither set.
5. In a group of 39 students, n(A) = 18, n(B) = 16, and n(A ∩ B) = 5. How many students are in neither A nor B?
10
By inclusion-exclusion, n(A ∪ B) = 18 + 16 − 5 = 29, leaving 39 − 29 = 10 in neither set.
6. In a group of 45 students, n(A) = 28, n(B) = 19, and n(A ∩ B) = 9. How many students are in neither A nor B?
7
By inclusion-exclusion, n(A ∪ B) = 28 + 19 − 9 = 38, leaving 45 − 38 = 7 in neither set.
7. In a group of 44 students, n(A) = 12, n(B) = 17, and n(A ∩ B) = 3. How many students are in neither A nor B?
18
By inclusion-exclusion, n(A ∪ B) = 12 + 17 − 3 = 26, leaving 44 − 26 = 18 in neither set.
8. In a group of 58 students, n(A) = 31, n(B) = 28, and n(A ∩ B) = 12. How many students are in neither A nor B?
11
By inclusion-exclusion, n(A ∪ B) = 31 + 28 − 12 = 47, leaving 58 − 47 = 11 in neither set.
9. In a group of 42 students, n(A) = 21, n(B) = 13, and n(A ∩ B) = 2. How many students are in neither A nor B?
10
By inclusion-exclusion, n(A ∪ B) = 21 + 13 − 2 = 32, leaving 42 − 32 = 10 in neither set.
10. In a group of 36 students, n(A) = 17, n(B) = 18, and n(A ∩ B) = 10. How many students are in neither A nor B?
11
By inclusion-exclusion, n(A ∪ B) = 17 + 18 − 10 = 25, leaving 36 − 25 = 11 in neither set.
11. In a group of 43 students, n(A) = 28, n(B) = 18, and n(A ∩ B) = 11. How many students are in neither A nor B?
8
By inclusion-exclusion, n(A ∪ B) = 28 + 18 − 11 = 35, leaving 43 − 35 = 8 in neither set.
12. In a group of 50 students, n(A) = 22, n(B) = 19, and n(A ∩ B) = 3. How many students are in neither A nor B?
12
By inclusion-exclusion, n(A ∪ B) = 22 + 19 − 3 = 38, leaving 50 − 38 = 12 in neither set.

12 questions · Seed 104733 · 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 40 students, n(A) = 28, n(B) = 18, and n(A ∩ B) = 11. How many students are in neither A nor B?
40 s · 28 · 18 · 11 · Universal set & Venn compl…
2. In a group of 33 students, n(A) = 14, n(B) = 14, and n(A ∩ B) = 6. How many students are in neither A nor B?
33 s · 14 · 14 · 6 · Universal set & Venn compl…
3. In a group of 59 students, n(A) = 25, n(B) = 29, and n(A ∩ B) = 9. How many students are in neither A nor B?
59 s · 25 · 29 · 9 · Universal set & Venn compl…
4. In a group of 48 students, n(A) = 29, n(B) = 20, and n(A ∩ B) = 9. How many students are in neither A nor B?
48 s · 29 · 20 · 9 · Universal set & Venn compl…
5. In a group of 39 students, n(A) = 18, n(B) = 16, and n(A ∩ B) = 5. How many students are in neither A nor B?
39 s · 18 · 16 · 5 · Universal set & Venn compl…
6. In a group of 45 students, n(A) = 28, n(B) = 19, and n(A ∩ B) = 9. How many students are in neither A nor B?
45 s · 28 · 19 · 9 · Universal set & Venn compl…
7. In a group of 44 students, n(A) = 12, n(B) = 17, and n(A ∩ B) = 3. How many students are in neither A nor B?
44 s · 12 · 17 · 3 · Universal set & Venn compl…
8. In a group of 58 students, n(A) = 31, n(B) = 28, and n(A ∩ B) = 12. How many students are in neither A nor B?
58 s · 31 · 28 · 12 · Universal set & Venn compl…
9. In a group of 42 students, n(A) = 21, n(B) = 13, and n(A ∩ B) = 2. How many students are in neither A nor B?
42 s · 21 · 13 · 2 · Universal set & Venn compl…
10. In a group of 36 students, n(A) = 17, n(B) = 18, and n(A ∩ B) = 10. How many students are in neither A nor B?
36 s · 17 · 18 · 10 · Universal set & Venn compl…
11. In a group of 43 students, n(A) = 28, n(B) = 18, and n(A ∩ B) = 11. How many students are in neither A nor B?
43 s · 28 · 18 · 11 · Universal set & Venn compl…
12. In a group of 50 students, n(A) = 22, n(B) = 19, and n(A ∩ B) = 3. How many students are in neither A nor B?
50 s · 22 · 19 · 3 · Universal set & Venn compl…

12 questions · Seed 104733 · 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 40 students, n(A) = 28, n(B) = 18, and n(A ∩ B) = 11. How many students are in neither A nor B?
5
By inclusion-exclusion, n(A ∪ B) = 28 + 18 − 11 = 35, leaving 40 − 35 = 5 in neither set.
2. In a group of 33 students, n(A) = 14, n(B) = 14, and n(A ∩ B) = 6. How many students are in neither A nor B?
11
By inclusion-exclusion, n(A ∪ B) = 14 + 14 − 6 = 22, leaving 33 − 22 = 11 in neither set.
3. In a group of 59 students, n(A) = 25, n(B) = 29, and n(A ∩ B) = 9. How many students are in neither A nor B?
14
By inclusion-exclusion, n(A ∪ B) = 25 + 29 − 9 = 45, leaving 59 − 45 = 14 in neither set.
4. In a group of 48 students, n(A) = 29, n(B) = 20, and n(A ∩ B) = 9. How many students are in neither A nor B?
8
By inclusion-exclusion, n(A ∪ B) = 29 + 20 − 9 = 40, leaving 48 − 40 = 8 in neither set.
5. In a group of 39 students, n(A) = 18, n(B) = 16, and n(A ∩ B) = 5. How many students are in neither A nor B?
10
By inclusion-exclusion, n(A ∪ B) = 18 + 16 − 5 = 29, leaving 39 − 29 = 10 in neither set.
6. In a group of 45 students, n(A) = 28, n(B) = 19, and n(A ∩ B) = 9. How many students are in neither A nor B?
7
By inclusion-exclusion, n(A ∪ B) = 28 + 19 − 9 = 38, leaving 45 − 38 = 7 in neither set.
7. In a group of 44 students, n(A) = 12, n(B) = 17, and n(A ∩ B) = 3. How many students are in neither A nor B?
18
By inclusion-exclusion, n(A ∪ B) = 12 + 17 − 3 = 26, leaving 44 − 26 = 18 in neither set.
8. In a group of 58 students, n(A) = 31, n(B) = 28, and n(A ∩ B) = 12. How many students are in neither A nor B?
11
By inclusion-exclusion, n(A ∪ B) = 31 + 28 − 12 = 47, leaving 58 − 47 = 11 in neither set.
9. In a group of 42 students, n(A) = 21, n(B) = 13, and n(A ∩ B) = 2. How many students are in neither A nor B?
10
By inclusion-exclusion, n(A ∪ B) = 21 + 13 − 2 = 32, leaving 42 − 32 = 10 in neither set.
10. In a group of 36 students, n(A) = 17, n(B) = 18, and n(A ∩ B) = 10. How many students are in neither A nor B?
11
By inclusion-exclusion, n(A ∪ B) = 17 + 18 − 10 = 25, leaving 36 − 25 = 11 in neither set.
11. In a group of 43 students, n(A) = 28, n(B) = 18, and n(A ∩ B) = 11. How many students are in neither A nor B?
8
By inclusion-exclusion, n(A ∪ B) = 28 + 18 − 11 = 35, leaving 43 − 35 = 8 in neither set.
12. In a group of 50 students, n(A) = 22, n(B) = 19, and n(A ∩ B) = 3. How many students are in neither A nor B?
12
By inclusion-exclusion, n(A ∪ B) = 22 + 19 − 3 = 38, leaving 50 − 38 = 12 in neither set.

12 questions · Seed 104733 · Age guidance, not curriculum certification