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Chapter 10: Problem 15

Does a set allow you to store duplicate elements?

Short Answer

Expert verified
Explain your answer. Answer: No, sets do not allow storing duplicate elements. A set is defined as a collection of distinct elements, meaning each element must be unique and appear only once. Even if there is an attempt to add a duplicate element, the set's properties do not allow it to be added, preserving the original form of the set.

Step by step solution

01

Definition of a Set

A set is a collection of distinct elements, which means that each element of the set is unique and appears only once. A set can contain any type of object, such as numbers, strings, or other sets, but the key characteristic of a set is that it does not allow for duplicate elements.
02

Determine if Sets Allow Duplicate Elements

Since a set is defined as a collection of distinct elements, it inherently does not allow the storage of duplicate elements. Each element within a set must be unique, so if there is an attempt to add a duplicate element, it will not be added to the set or replace any existing element.
03

Example 1: Set with Unique Elements

Let's work with an example of a set S with elements, S = {1, 2, 3, 4, 5}. In this case, each element is distinct, and there are no duplicate elements in the set.
04

Example 2: Adding Duplicate Elements to a Set

In another example, suppose we have set T = {1, 2, 3, 4, 5} and we try to add a duplicate element, say, the number 3. The new set would still be the same as the original set, meaning T = {1, 2, 3, 4, 5}. Even though we had attempted to add a duplicate element, the set's properties do not allow it to be added, preserving the original form of the set.
05

Conclusion

No, a set does not allow storing duplicate elements. It is a collection of distinct elements, meaning that each element in a set must be unique and appear only once.

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