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 44 students, n(A) = 28, n(B) = 23, and n(A ∩ B) = 12. How many students are in neither A nor B?
44 s · 28 · 23 · 12 · Universal set & Venn compl…
2. In a group of 33 students, n(A) = 17, n(B) = 24, and n(A ∩ B) = 11. How many students are in neither A nor B?
33 s · 17 · 24 · 11 · Universal set & Venn compl…
3. In a group of 42 students, n(A) = 19, n(B) = 32, and n(A ∩ B) = 12. How many students are in neither A nor B?
42 s · 19 · 32 · 12 · Universal set & Venn compl…
4. In a group of 52 students, n(A) = 23, n(B) = 21, and n(A ∩ B) = 9. How many students are in neither A nor B?
52 s · 23 · 21 · 9 · Universal set & Venn compl…
5. In a group of 33 students, n(A) = 19, n(B) = 15, and n(A ∩ B) = 10. How many students are in neither A nor B?
33 s · 19 · 15 · 10 · Universal set & Venn compl…
6. In a group of 39 students, n(A) = 13, n(B) = 13, and n(A ∩ B) = 4. How many students are in neither A nor B?
39 s · 13 · 13 · 4 · Universal set & Venn compl…
7. In a group of 49 students, n(A) = 23, n(B) = 21, and n(A ∩ B) = 4. How many students are in neither A nor B?
49 s · 23 · 21 · 4 · Universal set & Venn compl…
8. In a group of 49 students, n(A) = 23, n(B) = 19, and n(A ∩ B) = 6. How many students are in neither A nor B?
49 s · 23 · 19 · 6 · Universal set & Venn compl…
9. In a group of 49 students, n(A) = 22, n(B) = 17, and n(A ∩ B) = 2. How many students are in neither A nor B?
49 s · 22 · 17 · 2 · Universal set & Venn compl…
10. In a group of 42 students, n(A) = 19, n(B) = 16, and n(A ∩ B) = 4. How many students are in neither A nor B?
42 s · 19 · 16 · 4 · Universal set & Venn compl…
11. In a group of 40 students, n(A) = 16, n(B) = 19, and n(A ∩ B) = 10. How many students are in neither A nor B?
40 s · 16 · 19 · 10 · Universal set & Venn compl…
12. In a group of 26 students, n(A) = 10, n(B) = 14, and n(A ∩ B) = 2. How many students are in neither A nor B?
26 s · 10 · 14 · 2 · Universal set & Venn compl…

12 questions · Seed 49 · 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 44 students, n(A) = 28, n(B) = 23, and n(A ∩ B) = 12. How many students are in neither A nor B?
5
By inclusion-exclusion, n(A ∪ B) = 28 + 23 − 12 = 39, leaving 44 − 39 = 5 in neither set.
2. In a group of 33 students, n(A) = 17, n(B) = 24, and n(A ∩ B) = 11. How many students are in neither A nor B?
3
By inclusion-exclusion, n(A ∪ B) = 17 + 24 − 11 = 30, leaving 33 − 30 = 3 in neither set.
3. In a group of 42 students, n(A) = 19, n(B) = 32, and n(A ∩ B) = 12. How many students are in neither A nor B?
3
By inclusion-exclusion, n(A ∪ B) = 19 + 32 − 12 = 39, leaving 42 − 39 = 3 in neither set.
4. In a group of 52 students, n(A) = 23, n(B) = 21, and n(A ∩ B) = 9. How many students are in neither A nor B?
17
By inclusion-exclusion, n(A ∪ B) = 23 + 21 − 9 = 35, leaving 52 − 35 = 17 in neither set.
5. In a group of 33 students, n(A) = 19, n(B) = 15, and n(A ∩ B) = 10. How many students are in neither A nor B?
9
By inclusion-exclusion, n(A ∪ B) = 19 + 15 − 10 = 24, leaving 33 − 24 = 9 in neither set.
6. In a group of 39 students, n(A) = 13, n(B) = 13, and n(A ∩ B) = 4. How many students are in neither A nor B?
17
By inclusion-exclusion, n(A ∪ B) = 13 + 13 − 4 = 22, leaving 39 − 22 = 17 in neither set.
7. In a group of 49 students, n(A) = 23, n(B) = 21, and n(A ∩ B) = 4. How many students are in neither A nor B?
9
By inclusion-exclusion, n(A ∪ B) = 23 + 21 − 4 = 40, leaving 49 − 40 = 9 in neither set.
8. In a group of 49 students, n(A) = 23, n(B) = 19, and n(A ∩ B) = 6. How many students are in neither A nor B?
13
By inclusion-exclusion, n(A ∪ B) = 23 + 19 − 6 = 36, leaving 49 − 36 = 13 in neither set.
9. In a group of 49 students, n(A) = 22, n(B) = 17, and n(A ∩ B) = 2. How many students are in neither A nor B?
12
By inclusion-exclusion, n(A ∪ B) = 22 + 17 − 2 = 37, leaving 49 − 37 = 12 in neither set.
10. In a group of 42 students, n(A) = 19, n(B) = 16, and n(A ∩ B) = 4. How many students are in neither A nor B?
11
By inclusion-exclusion, n(A ∪ B) = 19 + 16 − 4 = 31, leaving 42 − 31 = 11 in neither set.
11. In a group of 40 students, n(A) = 16, n(B) = 19, and n(A ∩ B) = 10. How many students are in neither A nor B?
15
By inclusion-exclusion, n(A ∪ B) = 16 + 19 − 10 = 25, leaving 40 − 25 = 15 in neither set.
12. In a group of 26 students, n(A) = 10, n(B) = 14, and n(A ∩ B) = 2. How many students are in neither A nor B?
4
By inclusion-exclusion, n(A ∪ B) = 10 + 14 − 2 = 22, leaving 26 − 22 = 4 in neither set.

12 questions · Seed 49 · 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 44 students, n(A) = 28, n(B) = 23, and n(A ∩ B) = 12. How many students are in neither A nor B?
44 s · 28 · 23 · 12 · Universal set & Venn compl…
2. In a group of 33 students, n(A) = 17, n(B) = 24, and n(A ∩ B) = 11. How many students are in neither A nor B?
33 s · 17 · 24 · 11 · Universal set & Venn compl…
3. In a group of 42 students, n(A) = 19, n(B) = 32, and n(A ∩ B) = 12. How many students are in neither A nor B?
42 s · 19 · 32 · 12 · Universal set & Venn compl…
4. In a group of 52 students, n(A) = 23, n(B) = 21, and n(A ∩ B) = 9. How many students are in neither A nor B?
52 s · 23 · 21 · 9 · Universal set & Venn compl…
5. In a group of 33 students, n(A) = 19, n(B) = 15, and n(A ∩ B) = 10. How many students are in neither A nor B?
33 s · 19 · 15 · 10 · Universal set & Venn compl…
6. In a group of 39 students, n(A) = 13, n(B) = 13, and n(A ∩ B) = 4. How many students are in neither A nor B?
39 s · 13 · 13 · 4 · Universal set & Venn compl…
7. In a group of 49 students, n(A) = 23, n(B) = 21, and n(A ∩ B) = 4. How many students are in neither A nor B?
49 s · 23 · 21 · 4 · Universal set & Venn compl…
8. In a group of 49 students, n(A) = 23, n(B) = 19, and n(A ∩ B) = 6. How many students are in neither A nor B?
49 s · 23 · 19 · 6 · Universal set & Venn compl…
9. In a group of 49 students, n(A) = 22, n(B) = 17, and n(A ∩ B) = 2. How many students are in neither A nor B?
49 s · 22 · 17 · 2 · Universal set & Venn compl…
10. In a group of 42 students, n(A) = 19, n(B) = 16, and n(A ∩ B) = 4. How many students are in neither A nor B?
42 s · 19 · 16 · 4 · Universal set & Venn compl…
11. In a group of 40 students, n(A) = 16, n(B) = 19, and n(A ∩ B) = 10. How many students are in neither A nor B?
40 s · 16 · 19 · 10 · Universal set & Venn compl…
12. In a group of 26 students, n(A) = 10, n(B) = 14, and n(A ∩ B) = 2. How many students are in neither A nor B?
26 s · 10 · 14 · 2 · Universal set & Venn compl…

12 questions · Seed 49 · 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 44 students, n(A) = 28, n(B) = 23, and n(A ∩ B) = 12. How many students are in neither A nor B?
5
By inclusion-exclusion, n(A ∪ B) = 28 + 23 − 12 = 39, leaving 44 − 39 = 5 in neither set.
2. In a group of 33 students, n(A) = 17, n(B) = 24, and n(A ∩ B) = 11. How many students are in neither A nor B?
3
By inclusion-exclusion, n(A ∪ B) = 17 + 24 − 11 = 30, leaving 33 − 30 = 3 in neither set.
3. In a group of 42 students, n(A) = 19, n(B) = 32, and n(A ∩ B) = 12. How many students are in neither A nor B?
3
By inclusion-exclusion, n(A ∪ B) = 19 + 32 − 12 = 39, leaving 42 − 39 = 3 in neither set.
4. In a group of 52 students, n(A) = 23, n(B) = 21, and n(A ∩ B) = 9. How many students are in neither A nor B?
17
By inclusion-exclusion, n(A ∪ B) = 23 + 21 − 9 = 35, leaving 52 − 35 = 17 in neither set.
5. In a group of 33 students, n(A) = 19, n(B) = 15, and n(A ∩ B) = 10. How many students are in neither A nor B?
9
By inclusion-exclusion, n(A ∪ B) = 19 + 15 − 10 = 24, leaving 33 − 24 = 9 in neither set.
6. In a group of 39 students, n(A) = 13, n(B) = 13, and n(A ∩ B) = 4. How many students are in neither A nor B?
17
By inclusion-exclusion, n(A ∪ B) = 13 + 13 − 4 = 22, leaving 39 − 22 = 17 in neither set.
7. In a group of 49 students, n(A) = 23, n(B) = 21, and n(A ∩ B) = 4. How many students are in neither A nor B?
9
By inclusion-exclusion, n(A ∪ B) = 23 + 21 − 4 = 40, leaving 49 − 40 = 9 in neither set.
8. In a group of 49 students, n(A) = 23, n(B) = 19, and n(A ∩ B) = 6. How many students are in neither A nor B?
13
By inclusion-exclusion, n(A ∪ B) = 23 + 19 − 6 = 36, leaving 49 − 36 = 13 in neither set.
9. In a group of 49 students, n(A) = 22, n(B) = 17, and n(A ∩ B) = 2. How many students are in neither A nor B?
12
By inclusion-exclusion, n(A ∪ B) = 22 + 17 − 2 = 37, leaving 49 − 37 = 12 in neither set.
10. In a group of 42 students, n(A) = 19, n(B) = 16, and n(A ∩ B) = 4. How many students are in neither A nor B?
11
By inclusion-exclusion, n(A ∪ B) = 19 + 16 − 4 = 31, leaving 42 − 31 = 11 in neither set.
11. In a group of 40 students, n(A) = 16, n(B) = 19, and n(A ∩ B) = 10. How many students are in neither A nor B?
15
By inclusion-exclusion, n(A ∪ B) = 16 + 19 − 10 = 25, leaving 40 − 25 = 15 in neither set.
12. In a group of 26 students, n(A) = 10, n(B) = 14, and n(A ∩ B) = 2. How many students are in neither A nor B?
4
By inclusion-exclusion, n(A ∪ B) = 10 + 14 − 2 = 22, leaving 26 − 22 = 4 in neither set.

12 questions · Seed 49 · Age guidance, not curriculum certification