Question

After the following code executes, what elements will be members of set3? \\[\begin{array}{l}\text { set1 }=\operatorname{set}([10,20,30]) \\\\\text { set2 }=\operatorname{set}([100,200,300]) \\\\\text { set } 3=\text { set } 1 . \text { union (set2) }\end{array}\\]

Short answer

Answer: The elements of set3 are {10, 20, 30, 100, 200, 300}.

Step-by-step solution

Identify the elements in set1 and set2

Set1 has the elements {10, 20, 30} and set2 has the elements {100, 200, 300}.

Perform the union operation

The union operation, denoted by \(𝐴 \bigcup 𝐵\), combines all the elements of sets A and B, without any repetition. Thus, set3 will include all unique elements from both set1 and set2.

Find the elements of set3

By applying the union operation, set3 will include the unique elements from both set1 and set2: {10, 20, 30, 100, 200, 300}.

Key concepts

Union Operation in Python Sets

In Python, the union operation is a way to combine elements from multiple sets. When you perform a union, you bring together all the elements from these sets. The union operation is represented by the `|` operator or the `union()` method.
For instance, if you have two sets, say `setA` and `setB`, their union will result in a new set consisting of elements from both sets. To do this, you can either use `setA | setB` or `setA.union(setB)`.

• The union will not have duplicated elements. Even if an element appears in both `setA` and `setB`, it will appear only once in the union result.
• This operation is particularly useful when you want to consolidate elements and avoid redundancy.

By using the union operation, you can efficiently merge sets and ensure that the resulting collection has all the values, but just once. Here's a small example: ```python set1 = {1, 3, 5} set2 = {2, 3, 4} set3 = set1.union(set2) # Result: {1, 2, 3, 4, 5} ``` After applying the union, `set3` contains all distinct elements from both `set1` and `set2`. This approach ensures you gather all elements together without duplicates.

Understanding Set Data Structure in Python

A set in Python is a versatile data structure that is used to store multiple items in a single variable. One of its key features is that it automatically enforces uniqueness, meaning no member can appear more than once in a set.
Sets are defined by curly braces `{}` or the `set()` function, but empty sets can only be initialized with `set()` because `{}` is interpreted as an empty dictionary.

• Sets in Python are unordered, meaning the elements have no defined order.
• They are mutable, so you can add or remove elements after creation.
• Commonly used operations on sets include union, intersection, difference, and symmetric difference.

To illustrate, consider this example: ```python fruits = {'apple', 'banana', 'cherry'} fruits.add('orange') # Adds an element to the set print(fruits) # Output might vary in order ``` This shows how you can manage and manipulate collections of items without worry about duplicates. Sets are very handy when you need to ensure that the data you are dealing with is unique and unreplicated.

The Importance of Unique Elements in Sets

Unique elements are at the heart of the set data structure's functionality. A fundamental property of a set is that it cannot contain duplicate elements. This is inherent to the definition and behavior of sets, making them ideal for filtering out duplicates from a collection.
When working with data, having unique elements means:

• You can quickly determine membership, checking if an element is in the set is highly efficient.
• Duplicate entries are automatically eliminated, which streamlines data processing and analysis.
• Comparing sets through operations like union, intersection, and difference is both straightforward and powerful.

If you're handling operations where uniqueness is a requirement, such as eliminating duplicate names from a list or ensuring unique usernames, sets offer a perfect solution: ```python names = {'Alice', 'Bob', 'Alice', 'Eve'} print(names) # Output: {'Alice', 'Bob', 'Eve'} ``` Notice how "Alice" appears only once, demonstrating the automatic removal of duplicates in sets due to their requirement for unique membership.