Fill in the Venn Diagrams (Set 2) | Homeschool Books, Math ... - Free Printable

Let's solve each of the Venn diagram problems step by step. For each problem, we are given two sets, A and B, and we need to fill out the Venn diagram with:

- Elements only in A
- Elements only in B
- Elements in both A and B (the intersection)
- Elements that are in neither A nor B (if any) — but since no universal set is provided, we'll only place elements from A and B.

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🔹 General Steps:

1. Find the intersection: $ A \cap B $ → elements common to both A and B.
2. Find elements only in A: $ A - B $
3. Find elements only in B: $ B - A $
4. Place them in the appropriate regions of the Venn diagram.

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## ✔ Problem 1:
A: {12, 0, 2, 18, 3}
B: {9, 19, 0, 5, 12}

Step 1: Intersection

Common elements:
→ 0 and 12 are in both A and B
So, $ A \cap B = \{0, 12\} $

Step 2: Only in A

$ A - B = \{12, 0, 2, 18, 3\} - \{0, 12\} = \{2, 18, 3\} $

Step 3: Only in B

$ B - A = \{9, 19, 0, 5, 12\} - \{0, 12\} = \{9, 19, 5\} $

Final Diagram:

- Intersection (A ∩ B): 0, 12
- Only A: 2, 18, 3
- Only B: 9, 19, 5

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## ✔ Problem 2:
A: {14, 17, 0, 11, 1}
B: {20, 1, 11, 3, 14}

Step 1: Intersection

Common elements: 1, 11, 14
So, $ A \cap B = \{1, 11, 14\} $

Step 2: Only in A

$ A - B = \{14, 17, 0, 11, 1\} - \{1, 11, 14\} = \{17, 0\} $

Step 3: Only in B

$ B - A = \{20, 1, 11, 3, 14\} - \{1, 11, 14\} = \{20, 3\} $

Final Diagram:

- Intersection: 1, 11, 14
- Only A: 17, 0
- Only B: 20, 3

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## ✔ Problem 3:
A: {2, 17, 11, 14, 20}
B: {11, 6, 2, 10, 5}

Step 1: Intersection

Common elements: 2, 11
So, $ A \cap B = \{2, 11\} $

Step 2: Only in A

$ A - B = \{2, 17, 11, 14, 20\} - \{2, 11\} = \{17, 14, 20\} $

Step 3: Only in B

$ B - A = \{11, 6, 2, 10, 5\} - \{2, 11\} = \{6, 10, 5\} $

Final Diagram:

- Intersection: 2, 11
- Only A: 17, 14, 20
- Only B: 6, 10, 5

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## ✔ Problem 4:
A: {4, 12, 13, 6, 10}
B: {20, 12, 4, 5, 17}

Step 1: Intersection

Common elements: 4, 12
So, $ A \cap B = \{4, 12\} $

Step 2: Only in A

$ A - B = \{4, 12, 13, 6, 10\} - \{4, 12\} = \{13, 6, 10\} $

Step 3: Only in B

$ B - A = \{20, 12, 4, 5, 17\} - \{4, 12\} = \{20, 5, 17\} $

Final Diagram:

- Intersection: 4, 12
- Only A: 13, 6, 10
- Only B: 20, 5, 17

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## ✔ Problem 5:
A: {18, 5, 4, 14, 10}
B: {14, 4, 17, 8, 0}

Step 1: Intersection

Common elements: 4, 14
So, $ A \cap B = \{4, 14\} $

Step 2: Only in A

$ A - B = \{18, 5, 4, 14, 10\} - \{4, 14\} = \{18, 5, 10\} $

Step 3: Only in B

$ B - A = \{14, 4, 17, 8, 0\} - \{4, 14\} = \{17, 8, 0\} $

Final Diagram:

- Intersection: 4, 14
- Only A: 18, 5, 10
- Only B: 17, 8, 0

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## ✔ Problem 6:
A: {15, 20, 1, 8, 7}
B: {1, 20, 13, 2, 14}

Step 1: Intersection

Common elements: 1, 20
So, $ A \cap B = \{1, 20\} $

Step 2: Only in A

$ A - B = \{15, 20, 1, 8, 7\} - \{1, 20\} = \{15, 8, 7\} $

Step 3: Only in B

$ B - A = \{1, 20, 13, 2, 14\} - \{1, 20\} = \{13, 2, 14\} $

Final Diagram:

- Intersection: 1, 20
- Only A: 15, 8, 7
- Only B: 13, 2, 14

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📌 Summary Table

| Problem | A Only | B Only | Intersection |
|--------|--------------|--------------|------------------|
| 1 | 2, 18, 3 | 9, 19, 5 | 0, 12 |
| 2 | 17, 0 | 20, 3 | 1, 11, 14 |
| 3 | 17, 14, 20 | 6, 10, 5 | 2, 11 |
| 4 | 13, 6, 10 | 20, 5, 17 | 4, 12 |
| 5 | 18, 5, 10 | 17, 8, 0 | 4, 14 |
| 6 | 15, 8, 7 | 13, 2, 14 | 1, 20 |

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✔ How to Fill the Venn Diagrams:

For each diagram:
- Put intersection elements in the overlapping region.
- Put only A elements in the left non-overlapping part.
- Put only B elements in the right non-overlapping part.

You can now fill in the diagrams accordingly.

Let me know if you'd like a visual representation or printable version!