Venn Diagram - Two Circles worksheet for practicing set operations.

Let's solve each Venn diagram step by step using the standard set operations:

---

Venn Diagram 1: Sets A and B

Given:
- Circle A: Elements = {3, 6, 1, 4, 7}
- Circle B: Elements = {6, 1, 4, 8, 2, 5, 9}
- Intersection (A ∩ B): {6, 1, 4}

We'll use:
- A ∪ B = All elements in A or B or both
- A ∩ B = Elements in both A and B
- A − B = Elements in A but not in B
- B − A = Elements in B but not in A

#### Step-by-step:
- A ∪ B = {3, 6, 1, 4, 7, 8, 2, 5, 9} → All unique elements from both sets
So, A ∪ B = {3, 6, 1, 4, 7, 8, 2, 5, 9}

- A ∩ B = {6, 1, 4} → Elements common to both A and B
So, A ∩ B = {6, 1, 4}

- A − B = Elements only in A → {3, 7}
So, A − B = {3, 7}

- B − A = Elements only in B → {8, 2, 5, 9}
So, B − A = {8, 2, 5, 9}

---

Venn Diagram 2: Sets C and D

Given:
- Circle C: {b, f, i, d, e}
- Circle D: {i, k, a, j, c, d, y}
- Intersection (C ∩ D): {i, d}

#### Step-by-step:
- C ∪ D = All elements in C or D → {b, f, i, d, e, k, a, j, c, y}
So, C ∪ D = {a, b, c, d, e, f, i, j, k, y}

- C ∩ D = Common elements → {i, d}
So, C ∩ D = {i, d}

- C − D = Elements in C but not in D → {b, f, e}
So, C − D = {b, f, e}

- D − C = Elements in D but not in C → {k, a, j, c, y}
So, D − C = {a, c, j, k, y}

---

Venn Diagram 3: Sets E and F

Given:
- Circle E: {21, 9, 15, 3}
- Circle F: {24, 18, 6, 12, 15}
- Intersection (E ∩ F): {15}

#### Step-by-step:
- E ∪ F = All elements in E or F → {21, 9, 3, 15, 24, 18, 6, 12}
So, E ∪ F = {3, 9, 12, 15, 18, 21, 24}

- E ∩ F = Common element → {15}
So, E ∩ F = {15}

- E − F = Elements only in E → {21, 9, 3}
So, E − F = {3, 9, 21}

- F − E = Elements only in F → {24, 18, 6, 12}
So, F − E = {6, 12, 18, 24}

---

✔ Final Answers:

#### First Diagram (A and B):
- $ A \cup B = \{3, 6, 1, 4, 7, 8, 2, 5, 9\} $
- $ A \cap B = \{6, 1, 4\} $
- $ A - B = \{3, 7\} $
- $ B - A = \{8, 2, 5, 9\} $

#### Second Diagram (C and D):
- $ C \cup D = \{a, b, c, d, e, f, i, j, k, y\} $
- $ C \cap D = \{i, d\} $
- $ C - D = \{b, f, e\} $
- $ D - C = \{a, c, j, k, y\} $

#### Third Diagram (E and F):
- $ E \cup F = \{3, 9, 12, 15, 18, 21, 24\} $
- $ E \cap F = \{15\} $
- $ E - F = \{3, 9, 21\} $
- $ F - E = \{6, 12, 18, 24\} $

---

🔍 Explanation:

- Union (∪): Combine all elements from both sets, no duplicates.
- Intersection (∩): Only elements that appear in both sets.
- Difference (−): Elements in the first set but not in the second.

This method applies universally to any Venn diagram with two overlapping circles. Just identify regions and apply definitions accordingly.

Let me know if you'd like this formatted as a printable answer sheet!