### 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.

Answered: Image /qna-images/answer/6e78fe04-212e-4e1d-b805-8df95f00d0ef.jpg

1.2.1. Find the union C1UC2 and the intersection CilTC2 8I the two sets Ci and C2, where (a) C1 = {0, 1, 2, }, C2 = {2,3, 4}. (b) C1 = {r :0 < ¤ < 2}, C2 = {x :1< « < 3}. (c) C1 = {(x, y) :0 < x < 2,1 < y < 2}, C2 = {(x, y) :1< x < 3,1 < y < 3}.

1.2.1. Find the union C1UC2 and the intersection CilTC2 8I the two sets Ci and C2, where (a) C1 = {0, 1, 2, }, C2 = {2,3, 4}. (b) C1 = {r :0 < ¤ < 2}, C2 = {x :1< « < 3}. (c) C1 = {(x, y) :0 < x < 2,1 < y < 2}, C2 = {(x, y) :1< x < 3,1 < y < 3}.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

### 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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