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 39 students, n(A) = 9, n(B) = 18, and n(A ∩ B) = 4. How many students are in neither A nor B?
39 s · 9 · 18 · 4 · Universal set & Venn compl…
2. In a group of 44 students, n(A) = 25, n(B) = 11, and n(A ∩ B) = 6. How many students are in neither A nor B?
44 s · 25 · 11 · 6 · Universal set & Venn compl…
3. In a group of 33 students, n(A) = 11, n(B) = 15, and n(A ∩ B) = 3. How many students are in neither A nor B?
33 s · 11 · 15 · 3 · Universal set & Venn compl…
4. In a group of 31 students, n(A) = 8, n(B) = 18, and n(A ∩ B) = 4. How many students are in neither A nor B?
31 s · 8 · 18 · 4 · Universal set & Venn compl…
5. In a group of 43 students, n(A) = 28, n(B) = 19, and n(A ∩ B) = 8. How many students are in neither A nor B?
43 s · 28 · 19 · 8 · Universal set & Venn compl…
6. In a group of 25 students, n(A) = 11, n(B) = 11, and n(A ∩ B) = 4. How many students are in neither A nor B?
25 s · 11 · 11 · 4 · Universal set & Venn compl…
7. In a group of 53 students, n(A) = 17, n(B) = 30, and n(A ∩ B) = 11. How many students are in neither A nor B?
53 s · 17 · 30 · 11 · Universal set & Venn compl…
8. In a group of 53 students, n(A) = 19, n(B) = 25, and n(A ∩ B) = 9. How many students are in neither A nor B?
53 s · 19 · 25 · 9 · Universal set & Venn compl…
9. In a group of 47 students, n(A) = 11, n(B) = 22, and n(A ∩ B) = 3. How many students are in neither A nor B?
47 s · 11 · 22 · 3 · Universal set & Venn compl…
10. In a group of 36 students, n(A) = 14, n(B) = 26, and n(A ∩ B) = 8. How many students are in neither A nor B?
36 s · 14 · 26 · 8 · Universal set & Venn compl…
11. In a group of 39 students, n(A) = 17, n(B) = 14, and n(A ∩ B) = 4. How many students are in neither A nor B?
39 s · 17 · 14 · 4 · Universal set & Venn compl…
12. In a group of 32 students, n(A) = 12, n(B) = 20, and n(A ∩ B) = 6. How many students are in neither A nor B?
32 s · 12 · 20 · 6 · Universal set & Venn compl…

12 questions · Seed 46 · 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 39 students, n(A) = 9, n(B) = 18, and n(A ∩ B) = 4. How many students are in neither A nor B?
16
By inclusion-exclusion, n(A ∪ B) = 9 + 18 − 4 = 23, leaving 39 − 23 = 16 in neither set.
2. In a group of 44 students, n(A) = 25, n(B) = 11, and n(A ∩ B) = 6. How many students are in neither A nor B?
14
By inclusion-exclusion, n(A ∪ B) = 25 + 11 − 6 = 30, leaving 44 − 30 = 14 in neither set.
3. In a group of 33 students, n(A) = 11, n(B) = 15, and n(A ∩ B) = 3. How many students are in neither A nor B?
10
By inclusion-exclusion, n(A ∪ B) = 11 + 15 − 3 = 23, leaving 33 − 23 = 10 in neither set.
4. In a group of 31 students, n(A) = 8, n(B) = 18, and n(A ∩ B) = 4. How many students are in neither A nor B?
9
By inclusion-exclusion, n(A ∪ B) = 8 + 18 − 4 = 22, leaving 31 − 22 = 9 in neither set.
5. In a group of 43 students, n(A) = 28, n(B) = 19, and n(A ∩ B) = 8. How many students are in neither A nor B?
4
By inclusion-exclusion, n(A ∪ B) = 28 + 19 − 8 = 39, leaving 43 − 39 = 4 in neither set.
6. In a group of 25 students, n(A) = 11, n(B) = 11, and n(A ∩ B) = 4. How many students are in neither A nor B?
7
By inclusion-exclusion, n(A ∪ B) = 11 + 11 − 4 = 18, leaving 25 − 18 = 7 in neither set.
7. In a group of 53 students, n(A) = 17, n(B) = 30, and n(A ∩ B) = 11. How many students are in neither A nor B?
17
By inclusion-exclusion, n(A ∪ B) = 17 + 30 − 11 = 36, leaving 53 − 36 = 17 in neither set.
8. In a group of 53 students, n(A) = 19, n(B) = 25, and n(A ∩ B) = 9. How many students are in neither A nor B?
18
By inclusion-exclusion, n(A ∪ B) = 19 + 25 − 9 = 35, leaving 53 − 35 = 18 in neither set.
9. In a group of 47 students, n(A) = 11, n(B) = 22, and n(A ∩ B) = 3. How many students are in neither A nor B?
17
By inclusion-exclusion, n(A ∪ B) = 11 + 22 − 3 = 30, leaving 47 − 30 = 17 in neither set.
10. In a group of 36 students, n(A) = 14, n(B) = 26, and n(A ∩ B) = 8. How many students are in neither A nor B?
4
By inclusion-exclusion, n(A ∪ B) = 14 + 26 − 8 = 32, leaving 36 − 32 = 4 in neither set.
11. In a group of 39 students, n(A) = 17, n(B) = 14, and n(A ∩ B) = 4. How many students are in neither A nor B?
12
By inclusion-exclusion, n(A ∪ B) = 17 + 14 − 4 = 27, leaving 39 − 27 = 12 in neither set.
12. In a group of 32 students, n(A) = 12, n(B) = 20, and n(A ∩ B) = 6. How many students are in neither A nor B?
6
By inclusion-exclusion, n(A ∪ B) = 12 + 20 − 6 = 26, leaving 32 − 26 = 6 in neither set.

12 questions · Seed 46 · 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 39 students, n(A) = 9, n(B) = 18, and n(A ∩ B) = 4. How many students are in neither A nor B?
39 s · 9 · 18 · 4 · Universal set & Venn compl…
2. In a group of 44 students, n(A) = 25, n(B) = 11, and n(A ∩ B) = 6. How many students are in neither A nor B?
44 s · 25 · 11 · 6 · Universal set & Venn compl…
3. In a group of 33 students, n(A) = 11, n(B) = 15, and n(A ∩ B) = 3. How many students are in neither A nor B?
33 s · 11 · 15 · 3 · Universal set & Venn compl…
4. In a group of 31 students, n(A) = 8, n(B) = 18, and n(A ∩ B) = 4. How many students are in neither A nor B?
31 s · 8 · 18 · 4 · Universal set & Venn compl…
5. In a group of 43 students, n(A) = 28, n(B) = 19, and n(A ∩ B) = 8. How many students are in neither A nor B?
43 s · 28 · 19 · 8 · Universal set & Venn compl…
6. In a group of 25 students, n(A) = 11, n(B) = 11, and n(A ∩ B) = 4. How many students are in neither A nor B?
25 s · 11 · 11 · 4 · Universal set & Venn compl…
7. In a group of 53 students, n(A) = 17, n(B) = 30, and n(A ∩ B) = 11. How many students are in neither A nor B?
53 s · 17 · 30 · 11 · Universal set & Venn compl…
8. In a group of 53 students, n(A) = 19, n(B) = 25, and n(A ∩ B) = 9. How many students are in neither A nor B?
53 s · 19 · 25 · 9 · Universal set & Venn compl…
9. In a group of 47 students, n(A) = 11, n(B) = 22, and n(A ∩ B) = 3. How many students are in neither A nor B?
47 s · 11 · 22 · 3 · Universal set & Venn compl…
10. In a group of 36 students, n(A) = 14, n(B) = 26, and n(A ∩ B) = 8. How many students are in neither A nor B?
36 s · 14 · 26 · 8 · Universal set & Venn compl…
11. In a group of 39 students, n(A) = 17, n(B) = 14, and n(A ∩ B) = 4. How many students are in neither A nor B?
39 s · 17 · 14 · 4 · Universal set & Venn compl…
12. In a group of 32 students, n(A) = 12, n(B) = 20, and n(A ∩ B) = 6. How many students are in neither A nor B?
32 s · 12 · 20 · 6 · Universal set & Venn compl…

12 questions · Seed 46 · 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 39 students, n(A) = 9, n(B) = 18, and n(A ∩ B) = 4. How many students are in neither A nor B?
16
By inclusion-exclusion, n(A ∪ B) = 9 + 18 − 4 = 23, leaving 39 − 23 = 16 in neither set.
2. In a group of 44 students, n(A) = 25, n(B) = 11, and n(A ∩ B) = 6. How many students are in neither A nor B?
14
By inclusion-exclusion, n(A ∪ B) = 25 + 11 − 6 = 30, leaving 44 − 30 = 14 in neither set.
3. In a group of 33 students, n(A) = 11, n(B) = 15, and n(A ∩ B) = 3. How many students are in neither A nor B?
10
By inclusion-exclusion, n(A ∪ B) = 11 + 15 − 3 = 23, leaving 33 − 23 = 10 in neither set.
4. In a group of 31 students, n(A) = 8, n(B) = 18, and n(A ∩ B) = 4. How many students are in neither A nor B?
9
By inclusion-exclusion, n(A ∪ B) = 8 + 18 − 4 = 22, leaving 31 − 22 = 9 in neither set.
5. In a group of 43 students, n(A) = 28, n(B) = 19, and n(A ∩ B) = 8. How many students are in neither A nor B?
4
By inclusion-exclusion, n(A ∪ B) = 28 + 19 − 8 = 39, leaving 43 − 39 = 4 in neither set.
6. In a group of 25 students, n(A) = 11, n(B) = 11, and n(A ∩ B) = 4. How many students are in neither A nor B?
7
By inclusion-exclusion, n(A ∪ B) = 11 + 11 − 4 = 18, leaving 25 − 18 = 7 in neither set.
7. In a group of 53 students, n(A) = 17, n(B) = 30, and n(A ∩ B) = 11. How many students are in neither A nor B?
17
By inclusion-exclusion, n(A ∪ B) = 17 + 30 − 11 = 36, leaving 53 − 36 = 17 in neither set.
8. In a group of 53 students, n(A) = 19, n(B) = 25, and n(A ∩ B) = 9. How many students are in neither A nor B?
18
By inclusion-exclusion, n(A ∪ B) = 19 + 25 − 9 = 35, leaving 53 − 35 = 18 in neither set.
9. In a group of 47 students, n(A) = 11, n(B) = 22, and n(A ∩ B) = 3. How many students are in neither A nor B?
17
By inclusion-exclusion, n(A ∪ B) = 11 + 22 − 3 = 30, leaving 47 − 30 = 17 in neither set.
10. In a group of 36 students, n(A) = 14, n(B) = 26, and n(A ∩ B) = 8. How many students are in neither A nor B?
4
By inclusion-exclusion, n(A ∪ B) = 14 + 26 − 8 = 32, leaving 36 − 32 = 4 in neither set.
11. In a group of 39 students, n(A) = 17, n(B) = 14, and n(A ∩ B) = 4. How many students are in neither A nor B?
12
By inclusion-exclusion, n(A ∪ B) = 17 + 14 − 4 = 27, leaving 39 − 27 = 12 in neither set.
12. In a group of 32 students, n(A) = 12, n(B) = 20, and n(A ∩ B) = 6. How many students are in neither A nor B?
6
By inclusion-exclusion, n(A ∪ B) = 12 + 20 − 6 = 26, leaving 32 − 26 = 6 in neither set.

12 questions · Seed 46 · Age guidance, not curriculum certification