Naming Sets (A) Worksheet | Cazoom Maths Worksheets - Free Printable

Let's solve each of the 12 Venn diagram problems by identifying the correct set notation for the shaded regions. We'll use standard set operations:

- ∪ = union (elements in either set)
- ∩ = intersection (elements in both sets)
- A' = complement of A (everything not in A)
- The universal set is represented by the entire rectangle.

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1)

- Shaded: All of A, including overlap with B.
- This is A (since the whole circle A is shaded).
- ✔ Answer: A

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2)

- Shaded: All of B, including overlap with A.
- ✔ Answer: B

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3)

- Shaded: Everything outside both A and B → everything not in A or B.
- This is the complement of (A ∪ B).
- ✔ Answer: (A ∪ B)'

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4)

- Shaded: Only the overlapping region between A and B.
- ✔ Answer: A ∩ B

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5)

- Shaded: All of A, but not the part shared with B.
- That’s A minus the intersection with B.
- ✔ Answer: A \ B or A ∩ B'

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6)

- Shaded: Entire A and entire B → all elements in A or B.
- ✔ Answer: A ∪ B

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7)

- Shaded: Everything outside B, including parts of A and outside both.
- So it’s everything not in B.
- ✔ Answer: B'

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8)

- Shaded: Everything outside A, including parts of B and outside both.
- ✔ Answer: A'

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9)

- Shaded: Everything except the intersection of A and B.
- So it’s the complement of (A ∩ B).
- ✔ Answer: (A ∩ B)'

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10)

- Three sets: A, B, C
- Shaded: Only the region in C but not in A or B.
- So it’s C minus the parts in A or B.
- ✔ Answer: C ∩ A' ∩ B' or C \ (A ∪ B)

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11)

- Shaded: Everything outside A, including parts of B, C, and outside all.
- So it’s the complement of A.
- ✔ Answer: A'

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12)

- Shaded: Only the intersection of all three: A, B, and C.
- ✔ Answer: A ∩ B ∩ C

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✔ Final Answers:

| Question | Answer |
|--------|--------|
| 1 | A |
| 2 | B |
| 3 | (A ∪ B)' |
| 4 | A ∩ B |
| 5 | A \ B or A ∩ B' |
| 6 | A ∪ B |
| 7 | B' |
| 8 | A' |
| 9 | (A ∩ B)' |
| 10 | C ∩ A' ∩ B' or C \ (A ∪ B) |
| 11 | A' |
| 12 | A ∩ B ∩ C |

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🔍 Explanation Summary:

- Use union (∪) when combining sets.
- Use intersection (∩) for overlapping parts.
- Use complement (') for "not in".
- For differences like “A but not B”, write A ∩ B'.
- For three-set diagrams, think about which regions are included/excluded.

Let me know if you'd like a visual breakdown of any!