Practice set theory operations with this worksheet featuring union and intersection problems using integer sets.

Let’s go through each problem one by one. We’re working with sets — groups of numbers — and we need to find either the union (all elements from both sets, no duplicates) or the intersection (only elements that appear in both sets).

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Problem 1: Find B ∪ C

B = {14, 9, 10, -4, -11}
C = {-10, -4, -1, -12, -3, 10}

Union means combine all numbers from both sets, but write each number only once.

List all numbers:
From B: 14, 9, 10, -4, -11
From C: -10, -4, -1, -12, -3, 10

Now combine and remove duplicates:
-4 appears in both → keep once
10 appears in both → keep once

So union = {-12, -11, -10, -4, -3, -1, 9, 10, 14}
(We usually list them in order, though not required — but it helps avoid missing any.)

✔ Final for #1: {-12, -11, -10, -4, -3, -1, 9, 10, 14}

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Problem 2: Find E ∪ B

E = {6, 12, -3, -14, 1, -8}
B = {-8, 11, -12, 8, 7, 3}

Combine all numbers:

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

Duplicates? -8 is in both → keep once.

All together: {-14, -12, -8, -3, 1, 3, 6, 7, 8, 11, 12}

✔ Final for #2: {-14, -12, -8, -3, 1, 3, 6, 7, 8, 11, 12}

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Problem 3: Find J ∪ A

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

No overlapping numbers between J and A.

So just combine all:

{-15, -13, -10, -9, -3, -2, 0, 2, 3, 4, 8, 13}

✔ Final for #3: {-15, -13, -10, -9, -3, -2, 0, 2, 3, 4, 8, 13}

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Problem 4: Find F ∪ C

F = {14, -6, -1, -13, 0, 13}
C = {-1, 1, 2, -4, -14}

Common element? -1 is in both → keep once.

Combine all:

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

✔ Final for #4: {-14, -13, -6, -4, -1, 0, 1, 2, 13, 14}

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Problem 5: Find F ∩ A

F = {7, 1, 11, 4}
A = {11, -11, 4, 7}

Intersection = numbers that are in BOTH sets.

Check each:

- 7 → in F and A → yes
- 1 → only in F → no
- 11 → in both → yes
- 4 → in both → yes
- -11 → only in A → no

So intersection = {4, 7, 11}

✔ Final for #5: {4, 7, 11}

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Problem 6: Find D ∩ B

D = {14, -7, 9, -1}
B = {15, 14, -3, 12, -1, -7}

Check which numbers are in both:

- 14 → in D and B → yes
- -7 → in both → yes
- 9 → only in D → no
- -1 → in both → yes
- Others in B not in D → ignore

So intersection = {-7, -1, 14}

✔ Final for #6: {-7, -1, 14}

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Final Answer:
1. {-12, -11, -10, -4, -3, -1, 9, 10, 14}
2. {-14, -12, -8, -3, 1, 3, 6, 7, 8, 11, 12}
3. {-15, -13, -10, -9, -3, -2, 0, 2, 3, 4, 8, 13}
4. {-14, -13, -6, -4, -1, 0, 1, 2, 13, 14}
5. {4, 7, 11}
6. {-7, -1, 14}