Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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### Section 1.2.1: Set Operations

**Objective:** Find the union \( C_1 \cup C_2 \) and the intersection \( C_1 \cap C_2 \) of the two sets \( C_1 \) and \( C_2 \), where:

#### (a) Discrete Sets
- \( C_1 = \{0, 1, 2\} \)
- \( C_2 = \{2, 3, 4\} \)

#### (b) Continuous Sets on the Number Line
- \( C_1 = \{x : 0 < x < 2\} \)
- \( C_2 = \{x : 1 \leq x < 3\} \)

#### (c) Sets in the Cartesian Plane
- \( C_1 = \{(x, y) : 0 < x < 2, 1 < y < 2\} \)
- \( C_2 = \{(x, y) : 1 < x < 3, 1 < y < 3\} \)

**Explanation of Operations:**
- **Union (\( C_1 \cup C_2 \))**: Combines all elements from both sets without repetition.
- **Intersection (\( C_1 \cap C_2 \))**: Includes only elements that are present in both sets.

**Graphical Representation**:
- For continuous sets (b), visualize on a number line.
- For Cartesian plane sets (c), consider rectangles or regions on a plane.
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Transcribed Image Text:### Section 1.2.1: Set Operations **Objective:** Find the union \( C_1 \cup C_2 \) and the intersection \( C_1 \cap C_2 \) of the two sets \( C_1 \) and \( C_2 \), where: #### (a) Discrete Sets - \( C_1 = \{0, 1, 2\} \) - \( C_2 = \{2, 3, 4\} \) #### (b) Continuous Sets on the Number Line - \( C_1 = \{x : 0 < x < 2\} \) - \( C_2 = \{x : 1 \leq x < 3\} \) #### (c) Sets in the Cartesian Plane - \( C_1 = \{(x, y) : 0 < x < 2, 1 < y < 2\} \) - \( C_2 = \{(x, y) : 1 < x < 3, 1 < y < 3\} \) **Explanation of Operations:** - **Union (\( C_1 \cup C_2 \))**: Combines all elements from both sets without repetition. - **Intersection (\( C_1 \cap C_2 \))**: Includes only elements that are present in both sets. **Graphical Representation**: - For continuous sets (b), visualize on a number line. - For Cartesian plane sets (c), consider rectangles or regions on a plane.
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