Math worksheet for practicing set operations: finding the union and intersection of two given sets.

Let's solve each problem step by step.

We are asked to find:

- Union (A ∪ B): All elements that are in A, in B, or in both.
- Intersection (A ∩ B): Only the elements that are in both A and B.

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1. A = {2, 4, 6, 7, 10, 12, 14} and B = {3, 6, 9, 12, 15}

Union (A ∪ B):
Combine all elements from both sets without repetition.

- A has: 2, 4, 6, 7, 10, 12, 14
- B has: 3, 6, 9, 12, 15
- Common elements: 6, 12

So union includes all unique elements:
> A ∪ B = {2, 3, 4, 6, 7, 9, 10, 12, 14, 15}

Intersection (A ∩ B):
Only elements present in both sets:
- 6 and 12 are in both A and B

> A ∩ B = {6, 12}

✔ Answer:
- A ∪ B = {2, 3, 4, 6, 7, 9, 10, 12, 14, 15}
- A ∩ B = {6, 12}

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2. A = {5, 10, 15, 20, 25, 30, 35, 40} and B = {10, 20, 30, 40, 50, 60}

Union (A ∪ B):
All unique elements from both sets.

- A: 5, 10, 15, 20, 25, 30, 35, 40
- B: 10, 20, 30, 40, 50, 60
- Common: 10, 20, 30, 40

Union includes all:
> A ∪ B = {5, 10, 15, 20, 25, 30, 35, 40, 50, 60}

Intersection (A ∩ B):
Elements common to both:
- 10, 20, 30, 40

> A ∩ B = {10, 20, 30, 40}

✔ Answer:
- A ∪ B = {5, 10, 15, 20, 25, 30, 35, 40, 50, 60}
- A ∩ B = {10, 20, 30, 40}

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3. A = {a, b, d, e, g, h, m, o} and B = {d, e, f, g, h, i, j, k, l, m, n, o}

Union (A ∪ B):
All unique letters from both sets.

- A: a, b, d, e, g, h, m, o
- B: d, e, f, g, h, i, j, k, l, m, n, o
- Combine: Include all from A and any new from B

New in B: f, i, j, k, l, n

So:
> A ∪ B = {a, b, d, e, f, g, h, i, j, k, l, m, n, o}

Intersection (A ∩ B):
Common elements:
- d, e, g, h, m, o

> A ∩ B = {d, e, g, h, m, o}

✔ Answer:
- A ∪ B = {a, b, d, e, f, g, h, i, j, k, l, m, n, o}
- A ∩ B = {d, e, g, h, m, o}

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4. A = {2, 4, 6, 8} and B = {1, 3, 5, 7, 9, 11}

Union (A ∪ B):
All elements from both sets — no overlap.

- A: even numbers from 2 to 8
- B: odd numbers from 1 to 11

No common elements → just combine:
> A ∪ B = {1, 2, 3, 4, 5, 6, 7, 8, 9, 11}

Intersection (A ∩ B):
No element is in both sets → empty set

> A ∩ B = {} or ∅

✔ Answer:
- A ∪ B = {1, 2, 3, 4, 5, 6, 7, 8, 9, 11}
- A ∩ B = ∅

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5. A = {2, 4, 6, 8, 10} and B = {3, 4, 5, 7, 9, 11}

Union (A ∪ B):
All unique elements.

- A: 2, 4, 6, 8, 10
- B: 3, 4, 5, 7, 9, 11
- Common: 4

So combine:
> A ∪ B = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11}

Intersection (A ∩ B):
Only 4 is in both sets

> A ∩ B = {4}

✔ Answer:
- A ∪ B = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11}
- A ∩ B = {4}

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✔ Final Answers:

1.
- A ∪ B = {2, 3, 4, 6, 7, 9, 10, 12, 14, 15}
- A ∩ B = {6, 12}

2.
- A ∪ B = {5, 10, 15, 20, 25, 30, 35, 40, 50, 60}
- A ∩ B = {10, 20, 30, 40}

3.
- A ∪ B = {a, b, d, e, f, g, h, i, j, k, l, m, n, o}
- A ∩ B = {d, e, g, h, m, o}

4.
- A ∪ B = {1, 2, 3, 4, 5, 6, 7, 8, 9, 11}
- A ∩ B = ∅

5.
- A ∪ B = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11}
- A ∩ B = {4}

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