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Chapter 9: Problem 14

Are the elements of a set ordered or unordered?

Short Answer

Expert verified
Answer: The elements of a set are unordered.

Step by step solution

01

Understanding the concept of a set

A set is a collection of distinct objects, called elements or members, considered as an object in its own right. Sets are used to represent and study the relationships between different objects, and they are fundamental building blocks in many areas of mathematics.
02

Exploring the properties of a set

Sets have certain properties that can help us understand their nature: 1. Sets are unordered: The items in a set have no specific order, meaning that {a, b} and {b, a} are considered to be the same set. 2. Sets do not allow duplicate elements: Every item in a set must be unique. If a set contains duplicate elements, they are considered to be a single occurrence of that element. For example, the set {a, a, b} is equivalent to the set {a, b}.
03

Analyzing the question

To determine if the elements of a set are ordered or unordered, we can refer to the properties of sets mentioned above. Since sets are unordered, it means that the elements within a set have no specific order.
04

Conclusion

Based on the properties of sets, we can conclude that the elements of a set are unordered.

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