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Find AnB, the intersection of sets A and B. A={x: x is a natural number less than 4} B = {3, 4, 5, 6}

Find AnB, the intersection of sets A and B. A={x: x is a natural number less than 4} B = {3, 4, 5, 6}

Advanced Engineering Mathematics
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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**Title: Understanding Set Intersections** **Objective:** Learn how to find the intersection of two sets. **Problem Statement:** Find \( A \cap B \), the intersection of sets \( A \) and \( B \). **Definitions:** - Set \( A = \{x : x \text{ is a natural number less than 4}\} \) - Set \( B = \{3, 4, 5, 6\} \) **Solution:** The intersection of two sets, denoted \( A \cap B \), is the set of elements that are common to both \( A \) and \( B \). 1. **Identify the elements of set \( A \):** - Since \( A \) includes natural numbers less than 4, \( A = \{1, 2, 3\}\). 2. **Identify the elements of set \( B \):** - \( B = \{3, 4, 5, 6\} \) 3. **Find the common elements:** - The number 3 is present in both sets. Thus, the intersection \( A \cap B = \{3\} \). In conclusion, the intersection of sets \( A \) and \( B \) contains a single element, which is 3.
Transcribed Image Text:**Title: Understanding Set Intersections** **Objective:** Learn how to find the intersection of two sets. **Problem Statement:** Find \( A \cap B \), the intersection of sets \( A \) and \( B \). **Definitions:** - Set \( A = \{x : x \text{ is a natural number less than 4}\} \) - Set \( B = \{3, 4, 5, 6\} \) **Solution:** The intersection of two sets, denoted \( A \cap B \), is the set of elements that are common to both \( A \) and \( B \). 1. **Identify the elements of set \( A \):** - Since \( A \) includes natural numbers less than 4, \( A = \{1, 2, 3\}\). 2. **Identify the elements of set \( B \):** - \( B = \{3, 4, 5, 6\} \) 3. **Find the common elements:** - The number 3 is present in both sets. Thus, the intersection \( A \cap B = \{3\} \). In conclusion, the intersection of sets \( A \) and \( B \) contains a single element, which is 3.
Expert Solution
Step 1

Intersection of sets: It is the set of all those elements of the sets A and B which belong

to both the sets A and B. The intersection of two sets A and B is denoted by A∩B.

We have to find A∩B where A=x : x is a natural number less than 4 and

B=3, 4, 5, 6.

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