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Let's solve each problem step by step using set operations:

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1. Find $ B \cup C $

Given:
- $ B = \{14, 9, 10, -4, -11\} $
- $ C = \{-10, -4, -1, -12, -3, 10\} $

Union ($ \cup $): Combine all elements from both sets, removing duplicates.

List all elements from $ B $ and $ C $:
- From $ B $: 14, 9, 10, -4, -11
- From $ C $: -10, -4, -1, -12, -3, 10

Now combine and remove duplicates:
- Unique elements: -12, -11, -10, -4, -3, -1, 9, 10, 14

Order doesn't matter in sets, but we typically list them in ascending order for clarity.

✔ Answer:
$$
B \cup C = \{-12, -11, -10, -4, -3, -1, 9, 10, 14\}
$$

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2. Find $ E \cup B $

Given:
- $ E = \{6, 12, -3, -14, 1, -8\} $
- $ B = \{-8, 11, -12, 8, 7, 3\} $

Union: Combine all elements.

From $ E $: 6, 12, -3, -14, 1, -8
From $ B $: -8, 11, -12, 8, 7, 3

Combine and remove duplicates (note: -8 appears in both):

All unique elements: -14, -12, -8, -3, 1, 3, 6, 7, 8, 11, 12

✔ Answer:
$$
E \cup B = \{-14, -12, -8, -3, 1, 3, 6, 7, 8, 11, 12\}
$$

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3. Find $ J \cup A $

Given:
- $ J = \{-10, 0, 13, -9, 3, -15\} $
- $ A = \{-13, 8, -3, -2, 2, 4\} $

Union: Combine all elements.

From $ J $: -15, -10, -9, 0, 3, 13
From $ A $: -13, -3, -2, 2, 4, 8

No overlapping elements, so just combine:

All elements: -15, -13, -10, -9, -3, -2, 0, 2, 3, 4, 8, 13

✔ Answer:
$$
J \cup A = \{-15, -13, -10, -9, -3, -2, 0, 2, 3, 4, 8, 13\}
$$

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4. Find $ F \cup C $

Given:
- $ F = \{14, -6, -1, -13, 0, 13\} $
- $ C = \{-1, 1, 2, -4, -14\} $

Union: Combine all elements.

From $ F $: 14, -6, -1, -13, 0, 13
From $ C $: -1, 1, 2, -4, -14

Common element: -1

Combine all unique values:

-14, -13, -6, -4, -1, 0, 1, 2, 13, 14

✔ Answer:
$$
F \cup C = \{-14, -13, -6, -4, -1, 0, 1, 2, 13, 14\}
$$

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5. Find $ F \cap A $

Given:
- $ F = \{7, 1, 11, 4\} $
- $ A = \{11, -11, 4, 7\} $

Intersection ($ \cap $): Elements that are in both sets.

Compare:
- 7 → in both ✔
- 1 → only in F ✘
- 11 → in both ✔
- 4 → in both ✔

So common elements: 7, 11, 4

✔ Answer:
$$
F \cap A = \{4, 7, 11\}
$$

(Note: Order doesn't matter; we can write it as $\{4, 7, 11\}$ or any order.)

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6. Find $ D \cap B $

Given:
- $ D = \{14, -7, 9, -1\} $
- $ B = \{15, 14, -3, 12, -1, -7\} $

Find common elements:

Check each element of $ D $:
- 14 → in $ B $? Yes ✔
- -7 → in $ B $? Yes ✔
- 9 → in $ B $? No ✘
- -1 → in $ B $? Yes ✔

So common elements: 14, -7, -1

✔ Answer:
$$
D \cap B = \{-7, -1, 14\}
$$

(We can write in any order.)

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✔ Final Answers:

1. $ B \cup C = \{-12, -11, -10, -4, -3, -1, 9, 10, 14\} $
2. $ E \cup B = \{-14, -12, -8, -3, 1, 3, 6, 7, 8, 11, 12\} $
3. $ J \cup A = \{-15, -13, -10, -9, -3, -2, 0, 2, 3, 4, 8, 13\} $
4. $ F \cup C = \{-14, -13, -6, -4, -1, 0, 1, 2, 13, 14\} $
5. $ F \cap A = \{4, 7, 11\} $
6. $ D \cap B = \{-7, -1, 14\} $

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