Math worksheet for practicing union of sets with integer values.

It looks like you've uploaded a worksheet titled "Union of Sets: INTEGERS" with problems asking to find the union of two sets, denoted as $ X \cup Y $. The union of two sets includes all elements that are in either set (or both), without repetition.

Let me solve each problem step by step and explain the process.

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Instructions Recap:

For each pair of sets $ X $ and $ Y $, find $ X \cup Y $ — the union of the two sets.

We combine all unique elements from both sets.

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Problem 1:

- $ X = \{2, 12, 8, 13, 10\} $
- $ Y = \{3, 5, 12\} $

Solution:
Combine all elements:
- From $ X $: 2, 12, 8, 13, 10
- From $ Y $: 3, 5, 12

Now remove duplicates (12 appears in both):
→ $ X \cup Y = \{2, 3, 5, 8, 10, 12, 13\} $

✔ Answer: $ \{2, 3, 5, 8, 10, 12, 13\} $

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Problem 2:

- $ X = \{17, 15, 2, 1\} $
- $ Y = \{3, 14, 9\} $

No common elements.

Combine:
→ $ X \cup Y = \{1, 2, 3, 9, 14, 15, 17\} $

✔ Answer: $ \{1, 2, 3, 9, 14, 15, 17\} $

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Problem 3:

- $ X = \{2, 6, 8, 4, 10\} $
- $ Y = \{3, 5, 7, 8, 11\} $

Common element: 8

Combine:
→ $ X \cup Y = \{2, 3, 4, 5, 6, 7, 8, 10, 11\} $

✔ Answer: $ \{2, 3, 4, 5, 6, 7, 8, 10, 11\} $

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Problem 4:

- $ X = \{3, 2, 8, 16\} $
- $ Y = \{15, 1, 3, 8, 9\} $

Common elements: 3 and 8

Combine:
→ $ X \cup Y = \{1, 2, 3, 8, 9, 15, 16\} $

✔ Answer: $ \{1, 2, 3, 8, 9, 15, 16\} $

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Problem 5:

- $ X = \{3, 8, 9\} $
- $ Y = \{37, 4, 1\} $

No common elements.

→ $ X \cup Y = \{1, 3, 4, 8, 9, 37\} $

✔ Answer: $ \{1, 3, 4, 8, 9, 37\} $

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Problem 6:

- $ X = \{6, 3, 16\} $
- $ Y = \{6, 18, 2, 13\} $

Common element: 6

Combine:
→ $ X \cup Y = \{2, 3, 6, 13, 16, 18\} $

✔ Answer: $ \{2, 3, 6, 13, 16, 18\} $

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Problem 7:

- $ X = \{14, 12, 3, 2, 5\} $
- $ Y = \{6, 1, 10, 14, 17\} $

Common element: 14

Combine:
→ $ X \cup Y = \{1, 2, 3, 5, 6, 10, 12, 14, 17\} $

✔ Answer: $ \{1, 2, 3, 5, 6, 10, 12, 14, 17\} $

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Problem 8:

- $ X = \{10, 5, 11, 1\} $
- $ Y = \{3, 4, 6\} $

No common elements.

→ $ X \cup Y = \{1, 3, 4, 5, 6, 10, 11\} $

✔ Answer: $ \{1, 3, 4, 5, 6, 10, 11\} $

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Problem 9:

- $ X = \{7, 22, 8, 11, 14\} $
- $ Y = \{7, 11, 18, 9\} $

Common elements: 7, 11

Combine:
→ $ X \cup Y = \{7, 8, 9, 11, 14, 18, 22\} $

✔ Answer: $ \{7, 8, 9, 11, 14, 18, 22\} $

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Problem 10:

- $ X = \{18, 17, 8\} $
- $ Y = \{10, 18, 8, 12, 7\} $

Common elements: 18, 8

Combine:
→ $ X \cup Y = \{7, 8, 10, 12, 17, 18\} $

✔ Answer: $ \{7, 8, 10, 12, 17, 18\} $

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Problem 11:

- $ X = \{8, 12, 6\} $
- $ Y = \{18, 16, 10, 5, 18\} $

Note: 18 is repeated in $ Y $, but we only list it once.

No overlap between $ X $ and $ Y $.

→ $ X \cup Y = \{5, 6, 8, 10, 12, 16, 18\} $

✔ Answer: $ \{5, 6, 8, 10, 12, 16, 18\} $

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Problem 12:

- $ X = \{18, 8, 20, 5\} $
- $ Y = \{17, 18, 7, 10\} $

Common element: 18

Combine:
→ $ X \cup Y = \{5, 7, 8, 10, 17, 18, 20\} $

✔ Answer: $ \{5, 7, 8, 10, 17, 18, 20\} $

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✔ Final Answers Summary:

| Problem | $ X \cup Y $ |
|--------|----------------|
| 1 | {2, 3, 5, 8, 10, 12, 13} |
| 2 | {1, 2, 3, 9, 14, 15, 17} |
| 3 | {2, 3, 4, 5, 6, 7, 8, 10, 11} |
| 4 | {1, 2, 3, 8, 9, 15, 16} |
| 5 | {1, 3, 4, 8, 9, 37} |
| 6 | {2, 3, 6, 13, 16, 18} |
| 7 | {1, 2, 3, 5, 6, 10, 12, 14, 17} |
| 8 | {1, 3, 4, 5, 6, 10, 11} |
| 9 | {7, 8, 9, 11, 14, 18, 22} |
| 10 | {7, 8, 10, 12, 17, 18} |
| 11 | {5, 6, 8, 10, 12, 16, 18} |
| 12 | {5, 7, 8, 10, 17, 18, 20} |

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🔍 Key Concept:

The union of two sets combines all elements from both sets, removing duplicates. It's like merging two groups and making sure no one is listed twice.

Let me know if you'd like this formatted as a printable answer sheet or need help with intersection instead!